{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"top\"></a> \n",
    "# Filtering Field Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "_**Synopsis**_ \n",
    "\n",
    "**Data:** Ten 1 s trials of EEG data sampled at 1000 Hz.\n",
    "\n",
    "\n",
    "**Goal:** Filter these data to identify an evoked response.\n",
    "\n",
    "\n",
    "**Tools:** Fourier transform, convolution, magnitude response, frequency response, phase response.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Introduction](#.)\n",
    "* [Data analysis](#data-analysis)\n",
    "    1. [Visual inspection](#visual-inspection)\n",
    "    2. [Spectrial Analysis](#spectral-analysis)\n",
    "    2. [Evoked Response and Average Spectrum](#evoked-response)\n",
    "    3. [Naive Filtering](#naive-filters)\n",
    "    4. [More Sophisticated Filtering](#advanced-filters)\n",
    "    5. [What’s Phase Got to Do with It?](#phase)\n",
    "    6. [Analysis of the Filtered EEG Data](#analysis)\n",
    "* [Summary](#summary)\n",
    "* [Donate](#donate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## On-ramp: filtering field data in Python\n",
    "We begin this module with an \"*on-ramp*\" to analysis. The purpose of this on-ramp is to introduce you immediately to a core concept in this module: how to filter field data in Python. You may not understand all aspects of the program here, but that's not the point. Instead, the purpose of this on-ramp is to illustrate what *can* be done. Our advice is to simply run the code below and see what happens ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pylab import *\n",
    "from scipy.signal import firwin, lfilter, filtfilt\n",
    "from scipy.io import loadmat\n",
    "%matplotlib inline\n",
    "rcParams['figure.figsize']=(12,3)       # Change the default figure size\n",
    "\n",
    "data = loadmat('matfiles/EEG-1.mat')    # Load the data,\n",
    "eeg = data['EEG']              # ... and define the EEG,\n",
    "t = data['t'][0]               # ... and a time axis.\n",
    "\n",
    "dt = t[1] - t[0]               # Define the sampling interval.\n",
    "fNQ = 1 / dt / 2               # Determine the Nyquist frequency.\n",
    "K = len(eeg)                   # Determine no. of trials.\n",
    "\n",
    "n = 100                        # Define the filter order\n",
    "Wn = 30 / fNQ                  # ... and specify the cutoff frequency,\n",
    "b = firwin(n, Wn)              # ... build lowpass FIR filter,\n",
    "                               # ... and zero-phase filter each trial\n",
    "eeg_lo = array([filtfilt(b, 1, eeg[k]) for k in range(K)])\n",
    "\n",
    "mn = eeg_lo.mean(0)            # Compute mean of filtered EEG across trials (ERP)\n",
    "sd = eeg_lo.std(0)             # Compute std of filtered EEG data across trials.\n",
    "sdmn = sd / sqrt(K);           # Compute the std of the mean.\n",
    "\n",
    "plot(t, mn)                    # Plot the ERP of the filtered data\n",
    "plot(t, mn + 2 * sdmn, 'r:');  # ... and the confidence intervals,\n",
    "plot(t, mn - 2 * sdmn, 'r:');\n",
    "xlabel('Time [s]')             # ... and label the axes.\n",
    "ylabel('Voltage [ mV]')\n",
    "title('Evoked response of filtered EEG')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q:** Try to read the code above. Can you see how it loads data, lowpass filters it, and then plots the ERP of the filtered data?\n",
    "\n",
    "**A:** If you've never created and applied a filter before, that's an especially difficult question. Please continue on to learn this **and more**!\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "In previous case studies, we analyzed brain rhythms and discussed techniques to characterize these rhythms. Observed brain rhythms are often corrupted by noise. Sometimes this noise is obvious (e.g., electrical noise). In general, however, identifying the components of a brain signal that constitute signal versus noise is a difficult problem.\n",
    "\n",
    "In this module, we develop techniques to isolate, emphasize, or remove rhythmic activity in neural field data. To do so we introduce a broad area of study and research: **filtering**. In general, filtering is a very common procedure in the analysis of neural data. Although it is typically considered a preprocessing step, how filtering is performed may make or break subsequent analysis. This is a vast area, and we focus here on only some of the important concepts and tools.\n",
    "\n",
    "### Case study data\n",
    "Our colleague recorded the electroencephalogram (EEG) from a human subject during a task. After performing the experiment, he analyzed the data with the hope of finding an evoked response over visual cortex. However, his initial analysis suggested no evoked response. He therefore asked us to assist in his data analysis. He provided us with the EEG data recorded on the scalp surface above the left occipital lobe of one subject. He would like to understand the rhythmic features that appear in these data during the recording, and in particular whether an evoked response can be detected. He provided us with ten trials of EEG data, each of duration 1 s, recorded during the subject’s response to a visual stimulus (a small flash of light).\n",
    "\n",
    "### Goals\n",
    "Our goal is to better understand whether an evoked response appears in the data. We first make a visual inspection of the data, using techniques we developed to <a href=\"02\" rel=\"local\">study evoked responses</a>. However, our main goal is to understand the fundamental procedures of filtering neural field data, and we examine filtering methods applied to these example EEG data. We start by developing an intuitive approach to filtering and then implement and apply more sophisticated methods. We explain procedures to visualize filter properties and the resulting impact on the input signal.\n",
    "\n",
    "### Tools\n",
    "In this notebook, we rely on the Fourier transform (and associated measures) to develop a basic understanding of filters. If you are not confident using the Fourier transform, we strongly recommend reviewing notebooks <a href=\"03\" rel=\"local\">3</a> and <a href=\"04\" rel=\"local\">4</a>. This case study reinforces concepts in those notebooks and provides another opportunity to compute and to examine spectra, and to examine the relationships between the time and frequency domain representations of a time series. Upon completing this notebook, you should be familiar with basic filtering principles and methods to visualize the impact of filters, and equipped for further study and development of filtering procedures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.signal import firwin, lfilter, filtfilt\n",
    "from scipy.io import loadmat\n",
    "from pylab import *\n",
    "%matplotlib inline\n",
    "rcParams['figure.figsize']=(12,3)  # Change the default figure size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"data-analysis\"></a>\n",
    "## Data Visualization\n",
    "\n",
    "As always, let’s begin by looking at the data. To do so, we load the EEG data into Python and plot it:\n",
    "<a id=\"fig:1\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = loadmat('matfiles/EEG-1.mat')  # Load the EEG data\n",
    "eeg = data['EEG']            # Extract the EEG variable\n",
    "t = data['t'][0]             # ... and the t variable\n",
    "\n",
    "plot(t, eeg[0])              # Plot the data from the first trial versus time\n",
    "xlabel('Time [s]')           # Label the time axis\n",
    "ylabel('Voltage [mV]')       # ... and the voltage axis\n",
    "savefig('imgs/6-1.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that the variable `eeg` is a matrix, with each row corresponding to a single trial. Inspection of the variable `eeg` reveals there are 10 trials (i.e., 10 rows) each consisting of 1,000 indices. We also note that the visual stimulus is delivered just after the start of the trial (at time 0.001 s, corresponding to index 0 of variable `t`), and the response is recorded for the subsequent 1 s (the time 1 s corresponds to index 999 of variable `t`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** What are the sampling interval and sampling frequency of the EEG data?\n",
    "    \n",
    "**A.** Inspection of the variable `t`, loaded into Python, reveals that the sampling interval is 0.001 s, or 1 ms, and the sampling frequency is therefore 1/(0.001 s), or 1000 Hz.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visual inspection of the 1 s interval of the first trial suggests at least two distinct features. First, a rapid oscillation appears to occur, with amplitude near 1 mV. Second, a large deviation in voltage occurs (near 0.2 s). Additional slower oscillations may occur, although it’s difficult to tell from visual inspection alone."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Consider the fast rhythmic activity that dominates the EEG data plotted above. What is the frequency of this dominant rhythm? Do you observe an evoked response in this single trial? If so, where in time, and what features characterize the evoked response?\n",
    "    \n",
    "**A.** Careful counting of the number of peaks (or troughs) in the signal reveals that the fast rhythmic activity has a frequency of approximately 60 Hz. Visual inspection of the single-trial data does not suggest an evoked response (at least to the authors).\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** Examine other individual trials of the EEG data. Do you find features similar to those in the first trial?\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to top](#top)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"spectral-analysis\"></a>\n",
    "## Spectral Analysis\n",
    "\n",
    "Initial visual inspection of the single-trial data suggests that a 60 Hz rhythm dominates each individual trial. To further characterize this observation, let’s compute the spectrum of a single trial of EEG data <sup><abbr title=\"We could instead write the sample spectrum because this equation uses the observed data to estimate the theoretical spectrum that we would see if we kept repeating this experiment, but this distinction is not essential to the discussion here.\">note</abbr></sup>. We do so here for the first trial, and apply a Hanning taper before computing the spectrum (see <a href=\"04\" rel=\"local\">notebook 4</a>):\n",
    "\n",
    "<a id=\"fig:2\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = eeg[0]                # Load the first trial.\n",
    "x = x - x.mean()          # Subtract the mean from the data.\n",
    "dt = t[1] - t[0]          # Define the sampling interval.\n",
    "T = t[-1]                 # Define the duration of the trial.\n",
    "N = len(x)                # Define the number of points in the trial.\n",
    "\n",
    "xh = hanning(N) * x       # Multiply data by Hanning window,\n",
    "xf = rfft(xh)[:-1]        # ... compute Fourier transform,\n",
    "Sxx = 2 * dt ** 2 / T * (xf * xf.conj());  #... and compute spectrum.\n",
    "\n",
    "df = 1 / T;               # Determine frequency resolution.\n",
    "fNQ = 1 / dt / 2;         # Determine Nyquist frequency.\n",
    "faxis = arange(0, fNQ, df)              # Construct frequency axis\n",
    "\n",
    "semilogx(faxis, 10 * log10(Sxx.real))   # Plot decibels vs frequency,\n",
    "xlim([df, 100])           # ... in limited frequency range,\n",
    "xlabel('Frequency [Hz]')  # ... with axes labeled.\n",
    "ylabel('Power [dB]')\n",
    "title('Single-trial spectrum')\n",
    "savefig('imgs/6-2')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that in the second line of code, we remove the mean from the single trial of data. This is not always necessary but often useful; we are usually most interested in the rhythmic behavior of the EEG activity, not the changes in the mean signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** What is the resulting frequency resolution?\n",
    "\n",
    "**A.** The total duration of a trial is 1 s. Therefore the frequency resolution is 1/(1 s) = 1 Hz. If this answer makes no sense, we recommend reviewing the case study in <a href=\"03\" rel=\"local\">notebook 3</a>.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting spectrum reveals two important features. First, the power spectral density appears increased at lower frequencies compared to higher frequencies, that is, the spectrum tends to decrease with increasing frequency. This distribution of power is common in neural field data (e.g., [[He, et al., 2010]](https://doi.org/10.1016/j.neuron.2010.04.020)) and in other biological systems [[Bak, Tang, & Wiesenfeld, 1987]](https://doi.org/10.1103/PhysRevLett.59.381). Second, a large peak occurs at 60 Hz. This peak is consistent with the dominant rhythm apparent through visual inspection of the data in the first trial<a href=\"#fig:1\" class=\"sup\">fig<span><img src=\"imgs/6-1.png\"></span></a>.\n",
    "\n",
    "A 60 Hz peak is common in EEG data recorded in North America, where the alternating current in an electrical socket has frequency 60 Hz. We might also perhaps observe a second small peak between approximately 15 and 25 Hz. However, it’s not immediately apparent whether this peak represents a rhythm or a random fluctuation in the (noisy) spectrum. In any case, these initial spectral results are somewhat reassuring. The data exhibit characteristics we expect in typical scalp EEG data. Namely, the spectrum tends to decrease with frequency, and a large, sharp 60 Hz peak occurs, consistent with electrical noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** Examine the spectrum of other individual trials. Do you find features similar to those in trial 1?\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "\n",
    "<a id=\"evoked-response\"></a>\n",
    "## Evoked Response and the Average Spectrum\n",
    "\n",
    "Initial inspection of the features observable in the individual trials of EEG data has not been encouraging; the data appear to be dominated by 60 Hz line noise, with an occasional large-amplitude deviation. Through this initial inspection, it’s not clear whether an evoked response occurs in these data. We may therefore conclude that if an evoked response does occur in the data, the effect is weak and not apparent in a single trial. To further search for a weak evoked effect, let’s average the EEG responses across trials. In doing so, we hope that events unrelated to the stimulus will be reduced while responses evoked by the stimulus will be enhanced (see <a href=\"02\" rel=\"local\">notebook 2</a>). More specifically, let’s compute the mean and standard deviation of the mean EEG response at each time across trials:\n",
    "<a id=\"fig:3\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = len(eeg)                   # Define variable to record no. of trials\n",
    "mn = eeg.mean(0)               # Compute mean EEG across trials (ERP)\n",
    "sd = eeg.std(0)                # Compute std of EEG data across trials.\n",
    "sdmn = sd / sqrt(K);           # Compute the std of the mean.\n",
    "\n",
    "plot(t, mn)                    # Plot the ERP,\n",
    "plot(t, mn + 2 * sdmn, 'r:');  # ... and the confidence intervals,\n",
    "plot(t, mn - 2 * sdmn, 'r:');\n",
    "xlabel('Time [s]')             # ... and label the axes.\n",
    "ylabel('Voltage [ mV]')\n",
    "title('Evoked response')\n",
    "savefig('imgs/6-3a.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visual inspection suggests three important features. First, the 60 Hz rhythm, which dominated the individual trial data, is less prominent here. Second, large and brief increases in voltage appear in the ERP throughout the 1 s interval (e.g., at times near 0.2 s and at times near 0.8 s). Third, an interesting event appears near time 0.5 s, where we observe a brief interval of rhythmic fluctuations. The mean voltage appears to increase and decrease approximately twice in 125 ms, corresponding to an approximate 16 Hz rhythm. These mean results suggest an evoked response near time 0.5 s. However, we also observe that the 95% confidence intervals of the ERP include zero; we therefore do not find evidence for a significant ERP.\n",
    "\n",
    "In addition to the ERP, we also compute the trial-averaged spectrum: \n",
    "<a id=\"fig:3b\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def spectrum(x, t, hann=True):\n",
    "    '''\n",
    "    Define a function that computes the power spectrum \n",
    "    for any given x (trial data) and t (time of samples).\n",
    "    '''\n",
    "    dt = t[1] - t[0]\n",
    "    T  = t[-1]\n",
    "    x  = x - x.mean()\n",
    "    xh = hanning(N) * x if hann else x\n",
    "    xf = rfft(xh)[:-1]\n",
    "    Sxx = 2 * dt ** 2 / T * (xf * xf.conj())\n",
    "    return Sxx.real\n",
    "\n",
    "Sxx = [spectrum(trial, t, False) for trial in eeg] # Compute the spectrum for each trial.\n",
    "Sxxmn = array(Sxx).mean(0)                         # Convert the result into an array and compute the mean.\n",
    "semilogx(faxis, 10 * log10(Sxxmn))                 # Plot the result in decibels vs frequency,\n",
    "xlim([df, 100])                                    # ... in limited frequency range,\n",
    "ylim([-40,0])                                      # ... and limited power range,\n",
    "xlabel('Frequency [Hz]')                           # ... with axes labeled.\n",
    "ylabel('Power [dB]')\n",
    "title('Trial averaged spectrum')\n",
    "savefig('imgs/6-3b.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compared to the <a href=\"fig:2\" class=\"fig\">single-trial spectrum<span><img src=\"imgs/6-2.png\"></span></a>, the variability is greatly reduced in the <a href=\"fig:3b\" class=\"fig\">trial-averaged spectrum<span><img src=\"imgs/6-3b.png\"></span></a>. By reducing the variability in this way, the rhythmic peak between 15 Hz and 25 Hz becomes more apparent. We also observe both the 60 Hz electrical noise peak and the trend of decreasing power spectral density with increasing frequency, as in the single-trial spectrum."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** Given the initial analysis, what conclusions do you make regarding the EEG data?\n",
    "\n",
    "**A.** The analysis of the single-trial and trial-averaged results suggests that 60 Hz electrical noise dominates the EEG signal. We observe this electrical noise directly in the voltage traces and as a prominent sharp peak in the spectrum. We have some suggestive observations that an interesting evoked response may occur in the data but no conclusive (i.e., significant) evidence. Perhaps if we can reduce the 60 Hz electrical noise, we can uncover a weak evoked response that is currently hidden by the 60 Hz signal. To reduce the 60 Hz signal, we next try to filter these data.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "\n",
    "<a id=\"naive-filters\"></a>\n",
    "## Naive Filtering\n",
    "\n",
    "In this section, we introduce some fundamental concepts related to filtering. An easy approach to filtering is simply to use packaged Python functions to implement standard filtering methods. However, this approach can be dangerous. If we treat the filter as a black box, then we may not understand what a filter actually does and when it might fail to perform as we hope. To gain intuition for filtering, we therefore begin with a naive approach. This approach uses understanding of the Fourier transform and spectrum, and allows us to investigate how a simple filter performs. We then attempt to improve this naive approach, again using notions familiar from the study of spectra in previous notebooks (see notebooks <a href=\"03\" rel=\"local\">3</a> and <a href=\"04\" rel=\"local\">4</a>). Through this approach we do not implement the most sophisticated or useful filters; in fact, we do not recommend using this approach in practice. But we develop a deeper understanding of what a filter actually does. Later, we use packaged functions to implement standard filtering approaches. Ideally, these built-in functions will seem more interpretable with the knowledge gained through the initial naive filtering investigations.\n",
    "\n",
    "## A Naive Rectangular Filter\n",
    "\n",
    "Initial analysis of the data suggests that the dominant rhythmic activity is 60 Hz electrical noise. This activity is reassuring (we expect it) but also a nuisance; because the line noise is so dominant, other interesting features of lower amplitude may be masked. To search further for a weak evoked response in the data, we must reduce the dominant 60 Hz rhythm.\n",
    "\n",
    "We build our own filter to achieve this goal. The idea is simple: eliminate the 60 Hz rhythm from the EEG data. Recall that the Fourier transform converts a time domain representation of a signal to a frequency domain representation. Schematically, in symbols,\n",
    "\n",
    "<a id=\"eq:1\"></a>\n",
    "\n",
    "$$ \n",
    "  x_n \\xrightarrow{\\text{FT}} X_j \\tag{1}\n",
    "$$\n",
    "\n",
    "where $x_n$ is the data at each time index $n$, $X_j$ is the data at each frequency index $j$, and $FT$ denotes the Fourier transform. We also note that the inverse Fourier transform ($iFT$) converts the frequency domain representation of the data back to the time domain:\n",
    "\n",
    "$$\n",
    "   x_n \\xleftarrow{\\text{iFT}} X_j \\tag{2}\n",
    "$$\n",
    "<a id=\"eq:2\"></a>\n",
    "\n",
    "With these concepts, we may define three steps for a naive rectangular filter:\n",
    "\n",
    " 1. Move the observed EEG data to the frequency domain by computing the Fourier transform.\n",
    " 2. Set the frequency domain components of the EEG signal at 60 Hz to zero.\n",
    " 3. Move the altered data back to the time domain by computing the inverse Fourier transform.\n",
    " \n",
    "We call this initial approach a naive rectangular filter. We call it “naive” because we’re using naive intuition to construct the filter; we propose to eliminate the 60 Hz activity in the frequency domain in the simplest way and explore the consequences. We call it “rectangular” because we isolate abrupt intervals in the frequency domain to eliminate. Let’s attempt this procedure and examine the impact on the EEG data. \n",
    "\n",
    "### Step 1\n",
    "Our first step is to compute the Fourier transform of the EEG data. We focus specifically on the first trial; the same analysis can be performed on any individual trial. For completeness, we recompute some quantities from the previous sections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = eeg[0]        # Relabel the data from trial 1,\n",
    "x = x - x.mean()  # ... subtract the mean from the data, \n",
    "xf = fft(x)       # ... and compute the FT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** What are the dimensions of `xf`?\n",
    "\n",
    "**A.** Note that `xf` is a vector with the same dimensions as the original EEG data from trial 1 (labeled `x`). Remember that computing the Fourier transform of a signal does not alter its dimensions. However, also note that `xf` is a complex vector, consisting of both real and imaginary parts.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2\n",
    "\n",
    "We first define the frequency axis that corresponds to `xf`. We do so in the standard way implemented in previous notebooks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = t[1] - t[0]        # Define the sampling interval.\n",
    "N = len(x)              # Define the number of points in a single trial.\n",
    "faxis = fftfreq(N, dt)  # Construct the frequency axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we use the function `fftfreq()`, which first lists the positive frequencies, and then the\n",
    "negative frequencies. The construction is simimlar to traversing a circle whos angles are in the range of [$-\\pi$, $\\pi$]. If you start at zero, and rotate in a positive direction, you will eventually jump from $\\pi$ to $-\\pi$, and then continue. Let's visualize `faxis` computed with this function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(faxis)\n",
    "ylabel('Frequency (Hz)')\n",
    "xlabel('Index')\n",
    "title('Frequency axis')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the frequency axis (`faxis`) consists of both positive and negative frequencies. When examining the spectrum, we typically ignore the redundant negative frequencies. However, when developing a filter, we must be careful to include all frequencies. The frequency domain representation of the EEG data requires both positive and negative frequencies, and we must adjust both to filter the signal. Also notice that we use `fftfreq()` to easily compute the frequency axis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Consider the real and imaginary components of xf as a function of frequency. For each component, is the negative frequency axis a redundant representation of the positive frequency axis? *Hint*: Consider a plot of the imaginary component of `xf` versus frequency:\n",
    "\n",
    "    plot(faxis, xf.imag)\n",
    "\n",
    "What do you observe?\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the frequency axis defined, let’s now identify the indices corresponding to the 60 Hz rhythm we’d like to remove from the signal. Of the many approaches to perform this search, here’s one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find interval near 60 Hz.\n",
    "indices = (abs(faxis) >= 59) & (abs(faxis) <= 61)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In words, we find the indices where the absolute value of the frequency is between 59 and 61 (i.e., within 1 Hz of the target frequency, 60 Hz)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** Confirm that the values of `faxis` at the determined indices are less than, or equal to, 1 Hz from &plusmn;60 Hz.\n",
    "\n",
    "**A.** Executing the command: \n",
    "\n",
    "    faxis[indices]\n",
    "    \n",
    "we find two intervals of values: (-61, -60, -59) Hz, and (59, 60, 61) Hz, consistent with our expectations.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the indices surrounding the line noise frequency located, we’re ready to set the frequency domain components of the EEG signal at 60 Hz to zero. Let’s first define the filter in the frequency domain. This filter will have a value of 1 at all frequencies except near &plusmn;60 Hz, where we set the filter to 0. We then apply this filter to the frequency domain representation of the EEG data. By doing so, we set the (complex) values of `xf` (i.e., the frequency domain representation of the EEG data) to zero at the indices surrounding the line noise frequency. At all other indices, we leave `xf` unaltered (i.e., we multiply by 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "rectangular_filter = ones_like(x)      # Define filter in frequency domain\n",
    "rectangular_filter[indices] = 0        # ... set the filter at line-noise frequencies to zero\n",
    "xf_filtered = xf * rectangular_filter  # ... apply filter to data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before continuing, let’s visualize the filter and anticipate the impact on the frequency domain representation of the EEG data. We plot the variable `rectangular_filter`, the real part of `xf`, and their element-by-element product versus frequency.\n",
    "<a id=\"fig:4\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "isorted = argsort(faxis)                          # Sort the frequency axis\n",
    "plot(faxis[isorted], rectangular_filter[isorted]) # Plot rectangular filter vs frequency\n",
    "xlabel('Freq (Hz)')                               # ... with axes labeled\n",
    "ylabel('Naive square filter')\n",
    "title('Naive filter in frequency domain')\n",
    "xlim([-80, 80])\n",
    "savefig('imgs/6-4.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(faxis[isorted], xf.real[isorted], label=\"xf\") # Plot real part of xf\n",
    "                                                   # ... and real part of xf after filtering\n",
    "plot(faxis[isorted], xf_filtered.real[isorted], label='xf filtered')\n",
    "xlabel('Freq (Hz)')                                # ... with axes labeled\n",
    "ylabel('Real(xf)')\n",
    "title('Impact of naive filter on xf')\n",
    "xlim([-80, 80])\n",
    "legend()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"python-note\">\n",
    "\n",
    "Recall that `faxis` starts with the positive frequencies and then jumps to the negative frequencies. To display clearly the plots requires an additional step:\n",
    "\n",
    "    isorted = argsort(faxis)\n",
    "    \n",
    "where `isorted` are the indices that sort the frequency axis in ascending order. In the code above we use these indices to plot `rectangular_filter`, `xf` and `xf_filtered` according to the sorted values of `faxis`.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the filter maintains a value of 1 at all frequencies except for small intervals near &plusmn;60 Hz, where the filter has a value of 0. Considering the frequency domain representation of the EEG data, we observe that the real part of `xf` exhibits large peaks at &plusmn;60 Hz; these peaks correspond to the dominant 60 Hz rhythm apparent in the time domain EEG data. To apply the filter, we multiply the filter by the frequency domain representation of the data at each frequency. The result is shown in orange above. The peaks at &plusmn;60 Hz are eliminated because the value of the filter is set to 0 near these frequencies. All other frequency components in the EEG data are preserved, unaltered by the filter. The frequency domain representation of the EEG data also consists of an imaginary component, which we did not plot. However, the filter is applied to both the real and imaginary parts of `xf` through the element-by-element multiplication that defines `xf_filtered`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 3.\n",
    "\n",
    "Having eliminated the line noise in the frequency domain, we’re now ready to perform the third step of the naive rectangular filter. We apply the inverse Fourier transform, and transform the manipulated frequency domain signal back to the time domain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "xnew = ifft(xf_filtered)        # Compute iFT of freq domain data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** If the procedure behaves as expected, the resulting time domain signal `xnew` should be real and contain no imaginary components, consistent with the original EEG data. Is this so?\n",
    "\n",
    "**A.** To verify this, consider the command \n",
    "\n",
    "    max(xnew.imag)\n",
    "    \n",
    "You should find a value equal to (or within numerical precision of) zero.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand the behavior of the new filtered signal in the time domain, let’s plot it. \n",
    "<a id=\"fig:5a\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xnew = xnew.real                # The imag components are within numerical precision of 0.\n",
    "\n",
    "fig, ax = subplots()            # Save the resulting plots for later use\n",
    "plot(t, x, label='x')           # Plot the original signal\n",
    "ax.plot(t, xnew, label='xnew')  # ... and the filtered signal\n",
    "xlabel('Time (s)')              # ... with axes labeled\n",
    "ylabel('Voltage (mV)')\n",
    "fig.legend()\n",
    "savefig('imgs/6-5a.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An initial visual inspection suggests that the filter has the desired effect; the 60 Hz line noise is dramatically reduced. The same is true in the frequency domain. \n",
    "<a id=\"fig:5b\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute and plot the spectrum of the unfiltered signal.\n",
    "plot(arange(0, fNQ, df), 10 * log10(spectrum(x, t)), label='xf')\n",
    "# Compute and plot the spectrum of the filtered signal.\n",
    "plot(arange(0, fNQ, df), 10 * log10(spectrum(xnew.real, t)), label='xf_filtered')\n",
    "xlim([0, 100])\n",
    "xlabel('Freq (Hz)')\n",
    "ylabel('Power (dB)')\n",
    "legend()\n",
    "savefig('imgs/6-5b.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The spectrum of the original signal matches the spectrum of the filtered signal at all frequencies except near 60 Hz, where the power spectral density of the filtered signal is dramatically reduced.\n",
    "\n",
    "These initial observations suggest that the naive filter is performing quite well and achieving its intended purpose. Yet something is amiss. Consider an expanded view of the filtered signal near the large, brief increase in voltage at t &asymp; 0.2 s.\n",
    "<a id=\"fig:5c\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x216 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.lines.pop(0)         # Hide the plot of x\n",
    "ax.set_ylim([-.2, .5])  # Zoom in on the y-axis\n",
    "savefig('imgs/6-5c.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Do any features stand out in the plot above? Consider the voltage fluctuations near the large, brief increase in voltage in the filtered EEG data. What do you observe?\n",
    "\n",
    "**A.** Careful visual inspection suggests that near the abrupt voltage increase, small-amplitude oscillations emerge in the filtered signal. These oscillations appear to persist for an extended time interval around the abrupt amplitude deviation (at least 100 ms before and after the deviation) and have a period near 60 Hz.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might interpret the small-amplitude, approximately 60 Hz transient rhythms surrounding each large-amplitude deviation in the EEG data as a biological phenomenon. Perhaps the brain generates these coupled dynamics (i.e., the spike and surrounding rhythmic activity) to achieve a particular function. If so, this would be an important scientific result. However, let’s maintain some skepticism regarding the initial filter we’ve developed. Perhaps our filtering procedure is producing these small-amplitude rhythms around each spike; if so, these rhythms are an artifact of our analysis, not a biologically generated phenomenon. In what follows, we continue to explore the impact of the initial filter and suggest ways to further test the naive rectangular filter’s performance.\n",
    "\n",
    "### Impulse response\n",
    "\n",
    "So far we’ve characterized the naive rectangular filter by its impact in the frequency domain. To further characterize this filter, we examine its behavior in the time domain by computing the *impulse response*. As the name suggests, the impulse response indicates the filter’s response to a simple input signal consisting of a single brief impulse. The impulse, although simple in the time domain, possesses spectral content across a wide frequency range; it takes many sinusoids to represent a sharp object like an impulse. In this way, the impulse probes how the filter behaves to input with rich spectral content. We implement the impulse response as follows:\n",
    "<a id=\"fig:6a\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "impulse = zeros_like(rectangular_filter)  # Define the input signal,\n",
    "impulse[N // 2] = 1                          # ... with an impulse at the midpoint.\n",
    "impulsef = fft(impulse) * rectangular_filter # Apply naive filter,\n",
    "impulse_response = ifft(impulsef).real       # ... and iFT back to time domain\n",
    "lag_axis = arange(-N // 2, N // 2) * dt   # Define lag axis,\n",
    "\n",
    "fig, ax = subplots()                         # ... and plot the results.\n",
    "ax.plot(lag_axis, impulse_response, label=\"impulse response\")\n",
    "ax.plot(lag_axis, impulse, label=\"impulse\")\n",
    "xlabel('Time (s)')\n",
    "ylabel('Impulse response')\n",
    "legend()\n",
    "savefig('imgs/6-6a.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above, we see the original impulse and the impulse response (i.e., the result of applying the naive rectangular filter to the impulse). Visual inspection suggests how the filter affects the input signal in the time domain; we see that the filtered impulse consists of a large peak (centered at the time of the original impulse). By focusing on a small vertical range, we find that the peak at time 0 s is surrounded by smaller-amplitude fluctuations. \n",
    "<a id=\"fig:6b\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x216 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.set_ylim([-.01, .01])\n",
    "savefig('imgs/6-6b.png')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although these fluctuations are small, we notice that they persist across all time indices examined. By focusing both the vertical and horizontal range, we observe that these fluctuations are periodic, with a period of 60 Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 864x216 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.set_xlim([-.1, .1])\n",
    "savefig('imgs/6-6c.png')\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The impulse response provides important insights into the behavior of the naive rectangular filter: an impulse occurring in the original signal impacts all time points in the resulting filtered signal through small-amplitude 60 Hz fluctuations.\n",
    "\n",
    "We are concerned about this impulse response for the naive rectangular filter. We find that an impulse, initially localized to a single index in time, becomes broadly distributed in time upon filtering. To further illustrate the impact of the naive rectangular filter, let’s consider a more direct method to apply a filter and compute the impulse response. Up to this point, we applied the filter by first transforming the input signal to the frequency domain, then performing an element-by-element multiplication of the input signal and filter, and finally transforming the result back to the time domain. We can avoid these transformations by remembering the following important fact."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Multiplication in the frequency domain is equivalent to convolution in the time domain.**\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, as an alternative method for computing the impulse response, we convolve the impulse with the time domain representation of the filter. By doing so, we no longer need to transform to and from the frequency domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "i_rectangular_filter = ifft(rectangular_filter).real  # Transform the filter to the time domain,\n",
    "impulse_response_t = zeros_like(t)                    # ... and define the impulse response,\n",
    "for ii in range(N):                                   # ... at each time point\n",
    "    inds = [(ii - n) % N for n in range(N)]           # ... by computing the convolution\n",
    "    impulse_response_t[ii] = (i_rectangular_filter[inds] * impulse).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that in this code we compute the convolution by hand. We do so to make explicit the computation performed. At each time index (`ii`), we multiply element by element the shifted rectangular filter in the time domain (note the definition of `inds`) by the impulse. At each shift, we sum the elements of this product; the result is the impulse response at time index `ii`. Conceptually, we may visualize the convolution as multiplying shifted versions of the filter by the signal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "shift = 0                                          # Choose a shift,\n",
    "inds = [(shift - n) % N for n in range(N)]         # ... and define the indices,\n",
    "plot(i_rectangular_filter[inds], label=\"filter\")   # ... to plot the shifted rectangular filter.\n",
    "plot(impulse, label=\"impulse\")                     # Plot the impulse,\n",
    "legend()                                           # ... and compute the convolution at this shift.\n",
    "title('Convolution = {:.4f}'.format(sum(i_rectangular_filter[inds] * impulse)))\n",
    "ylim([-0.01, 0.1])\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When `shift = 0`, the filter begins with a peak at time index 0, and small oscillations are most apparent at lags near the beginning and end of the vector. As we (circularly) shift the filter, we move the filter peak to higher time indices (increase the value of `shift` in the code below to see this). When the filter peak reaches the impulse (`shift = 500`), the resulting summed product (i.e., the convolution) is large. Away from this time of large overlap, the resulting convolutions are small. The impulse response function is the result of these summed multiplications performed for all time shifts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting impulse response function computed in the time domain through convolution (variable name `impulse_response_t`, where `_t` denotes time) is identical to the impulse response function computed in the frequency domain through element-by-element multiplication (variable name `impulse_response`); we can see this by plotting `impulse_response_t` on the same axes where we previously plotted `impulse_response`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(lag_axis, impulse_response_t, '--', label='impulse_response_t')\n",
    "ax.legend()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now examined two equivalent methods of filter application: through multiplication in the frequency domain or through convolution in the time domain. Both approaches provide insight into the impact of the naive rectangular filter. The frequency domain representation is easier to interpret. We designed this filter in the frequency domain to eliminate signal components near 60 Hz, which we implemented through an abrupt decrease in the frequency domain representation of the filter. It’s relatively easy to envision that this filter eliminates signal features near &plusmn;60 Hz and preserves features at other frequencies<a href=\"#fig:4\" class=\"fig\"><sup>fig</sup><img src=\"imgs/6-4.png\"></a>.\n",
    "\n",
    "The time domain representation of the naive rectangular filter is more complicated. While the impact of the filter in the frequency domain is limited, the impact in the time domain is broad. The impulse response decays at times away from the impulse; however, these contributions do remain. This example illustrates the necessary trade-off between the time and frequency domains. Namely, the sharp transition bands, or roll-off in the frequency domain (i.e., the nearly vertical rectangular-shaped transitions) correspond to a broad impulse response function that extends over many lags in the time domain. There’s no escaping this fact: the sharper we make the filter’s transitions in the frequency domain, the broader its effects in time. Again, we make this trade-off to implement the sharp roll-off of the naive rectangular filter; the transition band is narrow (a precipitous drop) in frequency and therefore requires many values in time.\n",
    "\n",
    "Through the interpretation of filtering as convolution in time, we gain additional insight into the naive rectangular filter’s impact. When we looked closely, we identified suspicious behavior in the; we found that after filtering, the large-amplitude discharge was surrounded by small-amplitude oscillations with frequency near 60 Hz. Under the interpretation of filtering as convolution, we expect that a sudden large change in the input signal (i.e., the brief discharge in the EEG) will clearly impact the resulting filtered signal across an extended interval of time. Indeed, because the brief EEG discharge is so large, the small amplitude oscillations surrounding the central peak of the impulse function are apparent in the filtered EEG signal. For these brief large-amplitude peaks in the EEG data, the temporal impact of the filter is obvious in the filtered signal. However, this temporal impact occurs throughout the filtered signal; using the naive rectangular filter, each time point in the original signal impacts every time point in the [filtered signal](#fig:5c)<span class=\"fig\"><sup>fig</sup><img src=\"imgs/6-5c.png\"></span>.\n",
    "\n",
    "We conclude this section by noting that these results are analogous to our discussion of the rectangular window function in <a href=\"04\" rel=\"local\">notebook 4</a>. In that notebook, we applied a rectangular taper in the time domain and showed that this produced broad effects in the frequency domain. Here, we instead apply an (inverted) rectangular taper in the frequency domain and find broad effects in the time domain. The fundamental concept is that the Fourier transform of a sharp transition in one domain (in this case, the abrupt edge of a rectangular taper) produces broad effects in the other domain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "## A Naive Hanning filter\n",
    "\n",
    "In the previous section, we developed and applied a naive rectangular filter. We used the word “rectangular” to indicate the rectangular shape of the [filter](#fig:4)<span class=\"sup\">fig<img src=\"imgs/6-4.png\"></span> in the frequency domain. Although well-behaved in the frequency domain, the naive rectangular filter produces undesired effects in the time domain; namely, the filter’s sharp transitions in the frequency domain produce wide-ranging effects in the time domain. These long-range temporal effects are an unwanted feature of the filter. To reduce these effects, we propose an alternative filter that softens the sharp transitions in the frequency domain and makes these transitions more gradual. The idea is simple: replace the rectangular function in the original naive filter with a different, smoother function. In what follows we implement many of same procedures employed in the previous section and interpret how these changes affect the filtered EEG data.\n",
    "\n",
    "Let’s begin our filter design in the frequency domain. Our goal is to eliminate the 60 Hz component (i.e., the electrical noise) from the EEG signal without introducing long-lasting temporal effects. To do so, instead of the naive rectangular function employed in our first filter, we’ll use a smooth Hanning function (first introduced in our computations of the spectrum in <a href=\"04\" rel=\"local\">notebook 4</a>). First, we need to load the data and identify the indices corresponding to &plusmn;60 Hz, and then apply a Hanning window centered at each of these indices. Some of the following commands are redundant with commands we used previously, but they are repeated here for completeness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OGTMJ0zY313MXEZEcMHQUdOuJX6irxOnmF86DPv1g4OCoo4QmlXaLycAa59w659wJ4BHguqRtPNA18X03YGt4ETPH9OwdtFwsVJGcVquWwaEDwbLgIiIiaWJiRZgJF8LyxfhjR6KOk7f8wf2wchmmYirGmKjjhCaVIrk/sKnB482J5xq6G/iotXYzMBv4QijpImAqpsLm9fjtW6KOkrf8wlfVaiEiIhlhKqbByRP4pQuijpK3/OJEq0XFtKijhCqVnuTGPhL4pMc3Aw865/7TWnsh8D/W2tHOufdMTmitvQO4A8A5R0lJ9s2hVzfzGnb976/osKKSzqPHRh0nZcXFxVk5nsl8XS07l75Ju0nT6N4vO/u+c2Usc4XGM1waz3BpPMOTrWPpe17Erh4ltFm2kO5X3xh1nJRl63g2Zm/Vm9T1HUivcRV5dSY5lSJ5MzCwweMB/HU7xSeBKwGcc69ba9sDJcCOhhs552YBsxIP/a5du1qSOc1iMGQkh+c+y7EZH4g6TMpKSkrIzvF8L1+zBH9gHyfLJ2Vt3lwZy1yh8QyXxjNcGs/wZPNY+vEXcPyVZ9i5+W1M+45Rx0lJNo9nQ/7gfuLLFmOu+hC7d2fvWhP9+vVr9s+k0m6xABhmrR1srW1LcGPeE0nbvA1cBmCtHQW0B3Y2O02WUMtF+gStFh1gtJahFhGRzDATp6rlIk3ebbXIv/uMmiySnXO1wJ3AHGBF8JSrttbeY629NrHZl4FPW2uXAr8HbnfOJbdk5AwzIfg/WrNchMvX1eErX8eM1awWIiKSQfWzXOjveuj8onlwVn8YMCjqKKFLaZ7kxJzHs5Oe+3aD72uAvPkIYXqWJGa5eBWutlHHyR+rquDQwbyaQ1FERLKficUwE6fg587BHzuSMy0X2c4f2BfManHVh/KqF7meVtw7DVMxDTZvUMtFiPzCeWq1EBGRSJiKaVB7Ui0XIfKVbwStFpPy8+SXiuTTMBMSC4toAvJQBK0Wb6jVQkREojFkJHTvqbUQQnSq1aL/oKijpIWK5NM41XKxZH7UUfLDmppgAZHEqoYiIiKZZGIxzPgLoWYx/sTxqOPkPH/4EKxahpk4JS9bLUBF8hmZMZNg4xr8vj1RR8l5vmohFBdD6bioo4iISIEyYyfDiRPByq/SKr56McTjQa2Up1Qkn4EZUwGAX7Yw4iS5z1ctgOHlullCRESiM3w0tGsf/E2S1qlaAJ27wuBhUSdJGxXJZ9J/EPQsCc6CSov5Hdtg++ZTHzpERESiYNq0gVHj8FUL8D5nZ6qNnI/X4ZcvxpRPxMSKoo6TNiqSz8AYE1xGWLEEf/Jk1HFyVv2ZeFOuIllERKJlxlTAnl2wZWPUUXLXulVw+GBet1qAiuQmmfIKOH4M3loedZSc5asWQN+BmD59o44iIiIFrv6EjVouWs5XLYCiIigdH3WUtFKR3JSRY6BtW/0ytZA/dgRWLddZZBERyQqme084d6j+rreCr1oIQ0sxHTtFHSWtVCQ3wbRtByPHqn+ppWqWQl1t3l+SERGR3GHGVMC6t/AHD0QdJef43Ttgy8aC+LuuIjkFprwCdr0D2zdHHSXn+KoF0LFTMIm7iIhIFjBjJoGP46sXRR0l59RPZlAIN+OrSE7BqangdGmmWXw8jl+2EFM2AVNcHHUcERGRwDlDoGt30OxVzearFkCfvsFKe3lORXIKTM/eMGCQpoJrrrfXwoF9UACfNkVEJHeYWAxTXoGvXoyvrY06Ts7wx4/ByipMeUXerrLXkIrkFJkxk2BNTbAMo6TEVy0AE8OUTYw6ioiIyHuYMZPgyGFYuzLqKLljZRXUniyIfmRQkZwyM2YSxOPBMoySEl+1EIaMwHTpGnUUERGR9yodC8XFaqVsBl+1ANp1gOFlUUfJCBXJqRo8LFh+Ub9MKfH79sDGNZr6TUREspJp3xGGj1aRnCLvfXDyq2wcprhN1HEyQkVyikysCDN6QtC/FI9HHSfr1Z9xL4S7X0VEJDeZ8grYvhm/c3vUUbLflg2wb3dBnfxSkdwcZePh0EHYtC7qJNmvuhK69YT+g6JOIiIi0ihTNgEAv2JJxEmyn68Oxsjk+Sp7DalIbgZTOg4Av1x9yWfi43X4FUswpeMK4u5XERHJUWf3h5698dWVUSfJer56MfQ7B9OzJOooGaMiuRlM1x4wcDC+Rp84z+jtdcEZ97LC+bQpIiK5xxiDKRsPK6rwdXVRx8la/vhxWF1TUGeRQUVys5nS8bB2Jf7YkaijZK36T+Rm1NiIk4iIiJyZKR0HRw/DhtVRR8leq6uDqd/KxkWdJKNSWgbNWnslcB9QBDzgnLu3kW0scDfggaXOuVtCzJk1TNl4/JzHYFU1jC2MeQKby9csgXPOw3TtHnUUERGRMxs1FozBV1dihoyMOk1W8jWVUFwMw0ZHHSWjmjyTbK0tAu4HrgJKgZuttaVJ2wwDvgFMdc6VAV9KQ9bsMHQUtG0bvGHkr/hjR2DtyoK7JCMiIrnJdOoCg4bp7/oZ+JolMKwM065d1FEyKpV2i8nAGufcOufcCeAR4LqkbT4N3O+c2wvgnNsRbszsYdq0heHl+mU6nVXVUFd76iZHERGRbGdKx8H6t/BHtKpuMr9vN2zZGPRuF5hU2i36A5saPN4MnJ+0zXAAa+08gpaMu51zTyfvyFp7B3AHgHOOkpLcvEPy8ORpHPr1ffSIn6SoT9+o4wBQXFycFeN5YP0KjrZrT8kFFwUfKHJQtoxlvtB4hkvjGS6NZ3hyeSxPTJnB3icdXbZupP0F06OOA2TPeB6tepMDQI8pM2iTBXkyKZUiubE5vHwj+xkGXAIMAF6x1o52zu1ruJFzbhYwq34fu3btal7aLOHPHQbA7ldfIHbxFRGnCZSUlJAN41m38HUYPprd+w9EHaXFsmUs84XGM1waz3BpPMOTy2Ppe54F7Ttw4PWXOTQ0O5ZczpbxjM+fC127s69TN0wW5Gmpfv36NftnUmm32AwMbPB4ALC1kW3+7Jw76ZxbD6wiKJrzU9+B0L2XWi6S+F3vwDtb1GohIiI5xRQXw8gxwaq6Pvk8YOHy8Ti+JrHuQazwJkRL5V+8ABhmrR1srW0L3AQ8kbTN48AMAGttCUH7Rd4uSxfMqzgOVizFxzWvYr36+aMLsW9JRERymykdD7t3wM5tUUfJHpvWw6EDUKA34zdZJDvnaoE7gTnAiuApV22tvcdae21isznAbmttDfAi8FXn3O50hc4KpePhyGHYsCbqJFnD11RCjxI4e0DUUURERJqlfg7g+uWXhVNXzAv1CnFK8yQ752YDs5Oe+3aD7z3w94mvgmBGjcMbg6+pxJw3Iuo4kfPxOlixFDP+Qi1FLSIiuad3Xyg5KygMZ7w/6jRZwVdXwoDBmG49oo4SicJrMAmJ6dIVzhmiT5z1NqwJzqyr1UJERHKQMSZouVhZha+tjTpO5PzxY7BmRcGtsteQiuRWMGXjYd1K/JHDUUeJnK+uBGO0FLWIiOQsUzYejh2FdauijhK9VcsS6x4U7skvFcmtYErHQzwevJEKnK+phHOHYjp3jTqKiIhIy4wsh1hMs1eRuBm/TVsYVtr0xnlKRXJrDBkB7doX/C+TP3IY1q0q6E+bIiKS+0zHzjB4+KnZmgqZr66E4WU5uzBYGFQkt4IpbgMjyoM3UiFbtQzi8YLuWxIRkfxgSsfDhtX4wwejjhIZv3snbN9c8Ce/VCS3kikbDzu343cU7ryKvqYS2nUAzfIhIiI5zpSNB+9hxdKoo0Tm1NRvZRMiThItFcmtVP8pq5AvzfjqShhZHpxZFxERyWWDhkGHTgX9d52aJdC9J/Qb2PS2eUxFcmud1Q969SnYlgu/Yxvs3K5V9kREJC+YoiIYNbZgl6j28brEUtTjC37dAxXJrRTMqzgOVhXmvIrvrsajIllERPKDKRsHe3bB9i1RR8m8jWvhyCEo0FX2GlKRHAJTNh6OHoENb0UdJeN89RLo1Qf69I06ioiISCjMqMQS1QU4e9WpdQ9UJKtIDsXIsWBiBbf6nq+thVVVmDJdkhERkfxhep8NffoVZCulr6mEc4ZgunSLOkrkVCSHwHTqDIOHFd4nzg1vwdEjarUQEZG8Y8rGwapl+JMno46SMf7okcS6BzqLDCqSQ2NKx8P61fjDh6KOkjG+egmYGIwcE3UUERGRUJnS8XDiOKxbGXWUzFm1DOrqdDN+gorkkJiyceDjsLIq6igZ42sq4bzhwZl0ERGRfDKyHIqKCqrlIlj3oD2cNzLqKFlBRXJYBg2HDh3x1YujTpIR/vAhWL9al2RERCQvmfYdYcjIwiqSqyth+GhMG617ACqSQ2OKi2HEGHzNksKYV3HlUvBx9SOLiEjeMqXj4e21+IP7o46Sdn7ndtixTa0WDahIDpEpGw+7d8A7W6OOkna+uhI6dITBw6OOIiIikhaFtKpu/b9RRfK7VCSHqP6Nle+zXHjvg1+mkWOClYlERETy0bnnQacuwTLNec7XVELP3nBW/6ijZA0VySEyvc+G3mfn/yfOd7bC7h1qtRARkbxmYkWYUWPxNZV53Urp6+pghdY9SKYiOWSmbDysXIavzd95FU8tRa1LMiIiku9Kx8G+PbB1U9RJ0mfDajh6WDfjJ1GRHDJTOh6OH4W1q6KOkja+uhL69A3OnIuIiOSxU62UeTx7la9eHKx7MGps1FGySnEqG1lrrwTuA4qAB5xz955muw8BfwAmOecWhpYyl4wcA7EYvqYSM2J01GlC52tPwqplmAsvjTqKiIhI2pmevaHvwOAq6uXXRx0nLXzNEhg0FNOpS9RRskqTZ5KttUXA/cBVQClws7W2tJHtugBfBOaHHTKXmA4d4bw8nldx7So4fixYPEVERKQAmNJx8FY1/uSJqKOEzh85BOveUgtlI1Jpt5gMrHHOrXPOnQAeAa5rZLt/Af4DOBZivpxkysYl5lU8EHWU0PmaSojFYISWohYRkcJgysbDyROwuibqKOFbWaV1D04jlXaL/kDDbvXNwPkNN7DWjgcGOuf+z1r7ldPtyFp7B3AHgHOOkpKS5ifOASenzGDPn39Hly3raD9tZkaOWVxcnJHx3P3WMsyIcnoOPCftx4pKpsayUGg8w6XxDJfGMzz5PJb+wuns+Fkx7devosvF+fV3/cDalRzr0JGSSVOChdHklFRGo7G5QE7Ng2KtjQE/Am5vakfOuVnArPp97Nq1K4XD5x7fvQQ6duLAG3M5NDIzbQklJSWkezz9wQPE167CXHtz2o8VpUyMZSHReIZL4xkujWd48n4sh4ziyMLXOH7132TkcBn5u+498UWvwYhydu/bl9ZjRa1fv37N/plU2i02AwMbPB4ANFxSrgswGnjJWrsBuAB4wlpb0ew0ecLEimDU2LxbotqvXAreY8omRB1FREQko0zZBNi8Hr9/b9RRwrNzm9Y9OINUziQvAIZZawcDW4CbgFvqX3TO7QdOXQ+w1r4EfKVgZ7dIMGUT8Iteg22boF+etCZUL4aOneHcIVEnERERyShTNg7/2G/wNUswF86IOk4o6icZ0E17jWvyTLJzrha4E5gDrAiectXW2nustdemO2Cuqp+QO1+WqPbe46uXYEaNDc6Ui4iIFJIBg6FLN8iTv+uQKJJ7n43p0zfqKFkppQ5t59xsYHbSc98+zbaXtD5W7jO9+sDZ/fHVS2BmY5OB5Jhtm2DfbtCnTRERKUAmFsOMGhe0UsbjmFhur8fma2th5TLMBdOjjpK1cvv/4SxnSsfDW8vwJ3N/iepTS1FryUoRESlUZePgwD7YsjHqJK23bhUcP6p+5DNQkZxGpnQ8nDgBa3J/XkVfvQTO7h+cIRcRESlAp1op82CJ6lPrHowsjzpK1lKRnE4jRkNxMX55bv8y+ePHg6WoNauFiIgUMNO9F/Q/N+f/rgPBv+G8EZiOnaOOkrVUJKeRad8BhpfjqxZEHaV1VlXByROYMQU7q5+IiAgAZswkWFMTLOeco/y+3bBxTfBvkdNSkZxmZkwFbN+M37G16Y2zlK9aAO3aw7DRUUcRERGJlBlTAXV1QRtijvLLFgFgynXy60xUJKdZ/RvQV+XmtNHe+yB76ThMmzZRxxEREc8lQtcAABcOSURBVInWeSOgUxfI4avEvmoB9OwN/c+NOkpWU5GcZqZPX+g7EL8sN4tktmyAvbt0SUZERIRgVV1TPhG/fBE+Xhd1nGbzJ0/AiqWYMZMwxkQdJ6upSM4AU14Bq5bjjx2JOkqz+aXBJ2VdkhEREUkYMwkOHYD1q6NO0nyrlsPxY7rPKAUqkjPAjJkEdbVQk3v9S37ZQjh3KKZbj6ijiIiIZAVTNh5isZy8Md9XLYC2bWGEpn5riorkTBgyEjp0yrm+ZH/wAKxbpVYLERGRBkzHzjC0NPf+rnsfnPwaORbTtl3UcbKeiuQMMMXFmNET8MsW4uPxqOOkzC9fBN5jxqpIFhERaciMmQSb1+P37Iw6Suq2bYJd7+jkV4pUJGfKmIpgKcuNa6NOkrqqBdCtBww8L+okIiIiWaW+pzeXzibXt4foPqPUqEjOEFM2EYzBL8uN/iVfW4uvrsSUV2BiepuIiIi8x9kDoPfZOTV7lV+2EAYMxvQsiTpKTlD1kyGmS1c4b0TufOJcuwKOHtYlGRERkUYYY4K/kSuW4o8fjzpOk/zhg7Bmhf6uN4OK5AwyYybBxjX4fXuijtIkX7UAioth1Nioo4iIiGQlU14BJ0/AqqqoozTJL18M8bimfmsGFckZdKp/KQcuzfiqhTC8HNO+Q9RRREREstPw0dCufU78XWfZQujcFQYPizpJzlCRnEn9B0HP3vjKN6JOckZ++2bYvlmXZERERM7AtGkDZePxS+Zn9exVvvYkftlCTPlETKwo6jg5Q0VyBhljMBOnQM0S/JFDUcc5Lb/wVTAGM+HCqKOIiIhkNTNhCuzbA2tXRh3l9FYshSOHMROnRZ0kp6hIzjAzcSrU1eKXvBl1lNPyC+fBkFGYHr2ijiIiIpLVzNhJUNwGv2he1FFOyy+cBx06Qum4qKPkFBXJmXbeiKDlIkt/mfy2zbBlI6ZiatRRREREsp5p3xFGT8QvmpeVLRe+9iR+yRuYcecH7SGSsuJUNrLWXgncBxQBDzjn7k16/e+BTwG1wE7gE865jSFnzQv1LRf+hSfxRw4FS1tmEb+ovtViStRRREREcoKpmIpf8kbQcjGsNOo476VWixZr8kyytbYIuB+4CigFbrbWJr8DKoEK59wY4I/Af4QdNJ+YimlZ23KhVgsREZHmyeaWi6DVopNaLVoglXaLycAa59w659wJ4BHguoYbOOdedM4dSTx8AxgQbsw8M3h40HKx8NWok7zHu60W+rQpIiKSKtO+I5RnX8vFu60Wk9Vq0QKpFMn9gU0NHm9OPHc6nwSeak2ofGeMCXp+s2yWi1OtFhM1q4WIiEhzmIlTs2+Wi/pWC538apFUepJNI8/5xja01n4UqACmn+b1O4A7AJxzlJQU7trhJy+7mj3PPE7ntSvoMOOqVu+vuLi41eO5e8l8zKgx9Bw6otV5clkYYynv0niGS+MZLo1neAp9LOOXXsnOh35Cu+pFdL3w4lbvL4zx3L98Icc7dqbkopk6k9wCqRTJm4GBDR4PALYmb2StnQn8IzDdOdfoIubOuVnArMRDv2vXrualzSO+Rx/o2ZsDLz7F4fLWL9pRUlJCa8bTb9tMfONazE13tGo/+aC1YynvpfEMl8YzXBrP8GgsgbIJHJ33PMev/Qgm1roJxFr9d732JPE3XsaMPZ/d+/e3Kks+6NevX7N/JpUieQEwzFo7GNgC3ATc0nADa+144BfAlc65Hc1OUYDqWy788/+XFbNcqNVCRESkdczEqcGqutkwy8WpVgtN6dpSTX7Mcc7VAncCc4AVwVOu2lp7j7X22sRm3wc6A3+w1i6x1j6RtsR55N1ZLuZHHSW4+3XoKEx3zWohIiLSEmbsJGjTNituzPcLXtWsFq2U0jzJzrnZwOyk577d4PuZIecqDIOGQa8+wRt5ymWRxfBb3w5mtbjpjsgyiIiI5LpgYZEJ+EWv4e0nMUVFkeTwJ0/gl84PFhApVi9yS2nFvQgZYzDnT4fqSvyenZHl8K88C0VFmEm6JCMiItIasQsugf17YPmiyDL4Ra8FrRYXXBJZhnygIjli5qLLAR8UqhHwJ47jX38BM/5CTNcekWQQERHJG2MmQ7eexF9+OrIIfu7T0KcvjBwTWYZ8oCI5YqbkLCibgH/1GXxdXcaP7xe9BocPYi6+IuPHFhERyTemuBgzbSYsX4Tfnfm5DPzWt2F1DebiK1o9w0ah0+hlgdj0K4IJyKsWZPzYwafNfvq0KSIiEpLgKjH4V57J+LH93DlQXIyJ8F6nfKEiORuUT4LuvYjPzeylGb9lI6xZEXzaNI2tGSMiIiLNZXr1gdET8a8+h6+tzdhx39NC2aVbxo6br1QkZwFTVIS56H3BDXw7t2fsuP7lp/VpU0REJA1i068MbuCrejNjx/QLXw1u2Jve+pV8RUVy1jDTLgdMxi7N+OPH8G+8hJkwFdOla0aOKSIiUjBGT4QeJcRfnpOxQ/qXn4azB8DwsowdM5+pSM4SpmcJjKnAz8vMpRm/4BU4ehgzXTfsiYiIhM0UFWGmvQ9qKvE7tqX9eH7zeli3Si2UIVKRnEViF18BB/bB0vSvwOfnzoG+A2GYPm2KiIikg5n2PjCxjFwl9i/PgeI2mCmXpv1YhUJFcjYZPQF69k773Ir+7bWw/i192hQREUkj07MExk4KrhKfPJm24/hjR/HzX8JUTMN06pK24xQaFclZxMSKMJdcBSuW4teuTNtx4k/+Adp1wFw4I23HEBEREYjNeD8c3I9/NX1nk/2LT8LRI0ENIaFRkZxlzIyroWt34o8+iPc+9P37tSth8WuYKz6oT5siIiLpNmocjCjH/+UR/LEjoe/eHzqAf+pRGDsZM2Rk6PsvZCqSs4xp3wFzzU2wugaqFoa6b+898cd+A126Yd53Xaj7FhERkb9mjCF2423B2eRnHg99/372H+DYUWIfvDX0fRc6FclZyEy7HPr0I/7Yb/DxEJeqXrYQ3qrGXHMzpn2H8PYrIiIip2UGD4eJU/DPPI4/sDe0/frdO/AvPomZMgPT/9zQ9isBFclZyBQXE7vhVtj6Nv71l0LZp4/XEX/sIejT99RymSIiIpIZsetvhZMn8P/3v6Ht0//5YTAxzLW3hLZPeZeK5Gw1YQoMHo7/88P4E8dbvTv/+kuwZSPm+lsxxcWtzyciIiIpM2f3x1x0OX7uHPw7W1u9P79pfbAo2KUfwPTsHUJCSaYiOUud6mHauyu4a7UV/InjwafNQcMwFVNDSigiIiLNYa65GYqK8Y//ttX7ij/2EHTohLnqQyEkk8aoSM5iZkQ5lFfgZ/8Bv293i/fjn/kT7N1F7MbbNC+yiIhIREy3HpjLr8cvfBX/1vIW78cvWwTLF2He/2FMp84hJpSGVCRnudiHPw51ceI/vqdFU8f4Ra/hn/h9MMH4yDFpSCgiIiKpMpd/EHqfTfzn321R24XfspH4L78P/c7BzHh/GhJKPRXJWc70HUjsM1+DLRuJ/+I/8LW1Kf+sX7uS+K9+CIOHYz5+VxpTioiISCpMh47E7robgPiPv4M/eCDln/X7dhP/8XegbXtiX/xnTNt2aUopoCI5J5jyiZiPfA6WL8b/7r9SWmTEv7OV+E//Bbr3JHbnt/SLJCIikiXMWf2Iff5bsGcX8fv/NaUb9P2xI8R/fA8cPkzsi/+E6aWb9dItpWkOrLVXAvcBRcADzrl7k15vBzwETAR2A3/jnNsQbtTCFrv4CuK7dwSThvfqg7nannZbf3B/8EkTiN11N6ZLt0zFFBERkRSYoaOIferLxH/xPeK/+iGxz3wNEytqdFtfW0v8v74HWzYS+8I/Yc4ZkuG0hanJM8nW2iLgfuAqoBS42VpbmrTZJ4G9zrmhwI+A74UdVMBc/1HM5On4x39L3f3/hl/6Jr7u3cVG/N7dxJ90xP/ty7B3N7E7/wlzVr8IE4uIiMjpmIlTMB/+BCx+nfi9Xyc+7zn8saOnXvdHjxCf+zTx734VqisxH/kcZvTECBMXllTOJE8G1jjn1gFYax8BrgNqGmxzHXB34vs/Aj+11hrnXNN9AZIyYwzc/kXo1Rv/6rPEl8yHbj0x51/M3t07iC9+A3wcho8mdtsXtIa7iIhIljMzr4U2bfDP/QX/4I/xv/8lZvJF7C8uJj7veThxPLhJ7/a7iE29LOq4BSWVIrk/sKnB483A+afbxjlXa63dD/QCdjXcyFp7B3BHYjtKSkpaGLvA3fH3+E98keOL5nH0uf/jxHNPUNu9Jx1v+CgdLvsAxX0HRJ0wpxUXF+u9GSKNZ7g0nuHSeIZHY9kKH/oY/sZbObmiiqPP/4Vj817geKyIDtOvoMPMaygeVqopXCOQSpHc2P8ryWeIU9kG59wsYFb967t27UreRJpjSBkMKSN29Agl/fqxe+8+jgNoXFulpKQEvTfDo/EMl8YzXBrP8GgsQ9CnP9z8WWI3fpySkhJ2HzjICYDdLV8rQQL9+jW//TSV2S02AwMbPB4AJE/sd2oba20x0A3Y0+w00iKmQ0dMkZaaFhERyQembTvNSpUFUqmsFgDDrLWDgS3ATcAtSds8AdwGvA58CHhB/cgiIiIikquaPJPsnKsF7gTmACuCp1y1tfYea+21ic1+BfSy1q4B/h74h3QFFhERERFJN5PKwhRp4rdubf5yjNI49YKFR2MZLo1nuDSe4dJ4hkdjGS6NZ7gSPcnNuvtRK+6JiIiIiCRRkSwiIiIikiTSdouoDiwiIiIiBSc32i2stYsIwuorhC+Np8YyW780nhrPbP7SeGoss/VL45mW8WwWtVuIiIiIiCRRkSwiIiIikiTKInlW05tIM2g8w6OxDJfGM1waz3BpPMOjsQyXxjNczR7PKG/cExERERHJSmq3EBERERFJUpzpA1prxwH/BbQHaoG/dc69aa01wH3A+4EjwO3OucWZzpdrrLVfIFg2vBZ40jn3tcTz3wA+CdQBX3TOzYkuZW6x1n4F+D7Q2zm3S+/NlrHWfh+4BjgBrAU+7pzbl3hN789mstZeSfA+LAIecM7dG3GknGKtHQg8BJwNxIFZzrn7rLU9gf8FBgEbAOuc2xtVzlxirS0CFgJbnHMfsNYOBh4BegKLgVudcyeizJgrrLXdgQeA0QRT5H4CWIXemy1irf074FMEY7kM+DjQl2a+P6M4k/wfwHecc+OAbyceA1wFDEt83QH8PIJsOcVaOwO4DhjjnCsDfpB4vhS4CSgDrgR+lviPmTQh8Yf0fcDbDZ7We7NlngVGO+fGAG8B3wC9P1siMT73E7wXS4GbE+MoqasFvuycGwVcAHw+MYb/ADzvnBsGPJ94LKm5C1jR4PH3gB8lxnIvwQdhSc19wNPOuZHAWIJx1XuzBay1/YEvAhXOudEEJxZuogXvzyiKZA90TXzfDdia+P464CHnnHfOvQF0t9b2jSBfLvkccK9z7jiAc25H4vnrgEecc8edc+uBNcDkiDLmmh8BX+O9i93ovdkCzrlnnHO1iYdvAAMS3+v92XyTgTXOuXWJMx+PEIyjpMg5t63+CpBz7iBBEdKfYBx/k9jsN8D10STMLdbaAcDVBGc/SVxxuxT4Y2ITjWWKrLVdgYuBXwE4504krrrpvdlyxUAHa20x0BHYRgven1EUyV8Cvm+t3URw5vMbief7A5sabLc58Zyc3nDgImvtfGvty9baSYnnNZYtYK29luCy4dKklzSerfcJ4KnE9xrP5tOYhchaOwgYD8wHznLObYOgkAb6RBgtl/w/ghMK8cTjXsC+Bh+M9R5N3XnATuC/rbWV1toHrLWd0HuzRZxzWwjqy7cJiuP9wCJa8P5MS0+ytfY5gr6vZP8IXAb8nXPuUWutJfjkNJNgRZRkBT/1RhNjWQz0ILh0OAlw1trz0FieVhPj+U3g8kZe03iexpnG0zn358Q2/0hwqfvhxGsaz+bTmIXEWtsZeBT4knPuQPBnSJrDWvsBYIdzbpG19pLE03qPtlwxMAH4gnNuvrX2PtRa0WLW2h4EZ+EHA/uAPxC0qiVr8v2ZliLZOTfzdK9Zax8i6GOCIPgDie83AwMbbDqAd1sxClYTY/k54DHnnAfetNbGgRI0lqd1uvG01pYT/EItTfzRHAAsttZORuN5Wmd6fwJYa28DPgBclnifgsazJTRmIbDWtiEokB92zj2WePoda21f59y2RBvVjtPvQRKmAtdaa99PcBN+V4Izy92ttcWJs3V6j6ZuM7DZOTc/8fiPBEWy3pstMxNY75zbCWCtfQyYQgvenxmf3YIg1HTgJYL+kNWJ558A7rTWPgKcD+yvv8wgp/U4wRi+ZK0dDrQFdhGM5e+stT8E+hHccPZmZClzgHNuGQ0uZVlrNxA0/e+y1uq92QKJ2Ri+Dkx3zh1p8JLen823ABiWmD1gC8FNKLdEGym3JHpmfwWscM79sMFLTwC3Afcm/vfPEcTLKc65b/DujbiXAF9xzn3EWvsH4EMEPfMayxQ557ZbazdZa0c451YRXHGvSXzpvdl8bwMXWGs7AkcJxnMh8CLNfH9GUSR/Grgv0Ux9jGC2AIDZBFNsrSGYZuvjEWTLNb8Gfm2tXU4wzdZtibN11dZaR/ALVgt83jlXF2HOXKf3Zsv8FGgHPJs4O/+Gc+6zzjm9P5vJOVdrrb0TmENwp/avnXPVEcfKNVOBW4Fl1toliee+SVCAOGvtJwn+uH44onz54OvAI9bafwUqSdyIJin5AvCwtbYtsI7g70wMvTebLdGy8keCad5qCd6Ls4Anaeb7UyvuiYiIiIgk0Yp7IiIiIiJJVCSLiIiIiCRRkSwiIiIikkRFsoiIiIhIEhXJIiIiIiJJopgCTkREQmKtbUcwndGlzrntrdzXtcAtzrmbQgknIpLDNAWciEgrJRafOQtoON/zcOdc2lccs9Z+AShzzn028fhBgtW7vtVgm0HAeqBNYrWpM+1vOUGhXJW20CIiOUBnkkVEwnGNc+65M23QYEnUMH0m8RWW3xMs8nRniPsUEck5KpJFRNKkwRncTwH/DGwALrbWXgD8ECgFNgJ3OedeSvzMYOBBYALwBrAK6O6c+2gj+z8HGALMb0amfsBbDZ6KAR2ccybx+CXgt6hIFpECpyJZRCT9pgOjgLi1tj/B8qi3Ak8DlwGPWmtHOud2Ar8DXgcuB85PbPvn0+y3HFjXnLPTiRaQzvWPrbUP896buFcAg6y1XZ1zB1Ldr4hIvlGRLCISjsettfXF6kvOuesbvHa3c+4wgLX2o8Bs59zsxGvPWmsXAu+31r4ITAJmOueOA3OttX85wzG7Awcbef4r1tqGZ4IbncnIWvt1YCQwrcHT9fvrDqhIFpGCpSJZRCQc15+hJ3lTg+/PBT5srb2mwXNtgBeBfsDe+oI6YSMw8DT73Qt0aeT5H5zmxj0aPHcVcBdwvnPuaIOX6ve37zTHFBEpCCqSRUTSr+E0QpuA/3HOfTp5I2vtuUAPa22nBoXyOUk/31AVcF5zbwi01o4AfgPc4JzblPTyKGCDWi1EpNCpSBYRyazfAgustVcAzxGcRb4AWOOc25hovfiOtfabwGTgGuCJxnbknNtsrV2d2O61VA5ure1K0OP8Lefcq41sMh14qpn/JhGRvKMV90REMihx5vY64JvAToIzy1/l3f8e30Jww94eghkxHmpil78guAkwVROAEcAPrbWH6r8avH5zYp8iIgVNi4mIiGQxa+3dwNDGpoBLvF6/4t5lzrltrTzWNcCtzjnbmv2IiOQDtVuIiOSwxCwYpSHt6y/AmWbTEBEpGGq3EBERERFJonYLEREREZEkOpMsIiIiIpJERbKIiIiISBIVySIiIiIiSVQki4iIiIgkUZEsIiIiIpJERbKIiIiISJL/D7VeUvfvx2pmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = loadmat('matfiles/EEG-1.mat')  # Load,\n",
    "eeg = data['EEG']            # ... the EEG data,\n",
    "t = data['t'][0]             # ... and the time axis.\n",
    "x = eeg[0]                   # Analyze the first trial.\n",
    "dt = t[1] - t[0]             # Define the sampling interval.\n",
    "N = len(x)                   # Define the no. of points in a single trial.\n",
    "df = 1 / (N * dt)            # Determine the frequency resolution.\n",
    "fNQ = 1 / dt / 2             # Determine the Nyquist frequency.\n",
    "faxis = fftfreq(N, dt)       # Construct the frequency axis.\n",
    "\n",
    "win = 15                     # Set the size of the Hann window,\n",
    "                             # ... and find indices within win of 60 Hz.\n",
    "inds = (abs(faxis) >= (60 - win * df)) & (abs(faxis) <= (60 + win * df))\n",
    "\n",
    "hann_filter = ones_like(t)   # Define filter in frequency domain.\n",
    "hann_filter[inds] = hstack([1 - hanning(2 * win + 1), 1 - hanning(2 * win + 1)])\n",
    "\n",
    "isorted = argsort(faxis)                     # Sort the frequency axis.\n",
    "plot(faxis[isorted], hann_filter[isorted])   # Plot the filter.\n",
    "xlim([-80, 80])\n",
    "xlabel('Freq (Hz)')\n",
    "title('Hanning filter')\n",
    "savefig('imgs/6-8a')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this code, we load the EEG from the first trial (variable `x`) and create the frequency axis (variable `faxis`) to find the indices that correspond to frequencies at &plusmn;60 Hz. At these indices, we center a Hanning window, which sets the filter to 0 at &plusmn;60 and gradually returns to 1 away from these values (the parameter `win` sets the width of the window)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** Plot the original naive rectangular filter on top of the new Hanning filter. Compare the frequency domain representations of the two filters. What differences do you observe?\n",
    "\n",
    "**A.** Although both filters decrease to 0 near ±60 Hz, the Hanning filter returns gradually to 1, while the rectangular filter rapidly changes from 0 to 1. In other words, the roll-off is more gradual in the Hanning filter compared to the square filter.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s also examine the time domain representation of the new Hanning filter. To do so, we compute the impulse response.\n",
    "<a id=\"fig:8b\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def convolution(impulse, filt):\n",
    "    '''\n",
    "    Compute the impulse response of a filter (given in the \n",
    "    time domain) using convolution.\n",
    "    '''\n",
    "    N = len(impulse)\n",
    "    response = zeros_like(impulse)\n",
    "    for ii in range(N):\n",
    "        inds = [(ii + n) % N for n in range(N)]\n",
    "        response[ii] = sum(impulse[inds] * filt)\n",
    "    return response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "impulse = zeros_like(x)                 # Define the input signal,\n",
    "impulse[N // 2] = 1                     # ... with impulse at the midpoint\n",
    "i_hann_filter = ifft(hann_filter).real  # Transform filter to time domain,\n",
    "                                        # ... and compute the impulse response by convolution.\n",
    "impulse_response_t = convolution(i_hann_filter, impulse)\n",
    "lag_axis = arange(-N/2, N/2) * dt       # Define the lag axis for plotting\n",
    "plot(lag_axis, impulse_response_t)      # Display the result\n",
    "xlabel('Time (s)')\n",
    "ylabel('Impulse response')\n",
    "ylim([-.03, .05])\n",
    "savefig('imgs/6-8b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this code, we first define the impulse signal and then convolve this impulse with the Hanning filter transformed to the time domain (using `ifft`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Plot the time domain representation of the original naive rectangular filter on top of that of the new Hanning filter. Compare the two. What differences do you observe?\n",
    "\n",
    "**A.** To answer this question, execute the commands below. You'll find that both filters exhibit a large peak at time 0 s and are surrounded by small-amplitude 60 Hz oscillations. Compared to the naive rectangular filter, these oscillations are initially larger for the proposed Hanning filter. However, these oscillations quickly decay for the Hanning filter; after ±50 ms, the Hanning filter remains near zero.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the time domain representations of the naive rectangular and Hanning filters.\n",
    "plot(ifft(hann_filter).real,        label=\"Hanning filter in time domain\")\n",
    "plot(ifft(rectangular_filter).real, label=\"Rectangular filter in time domain\")\n",
    "legend()\n",
    "ylim([-0.05,0.05])\n",
    "xlim([0,500]);\n",
    "xlabel('Time (indices)')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Compute the impulse response function of the Hanning filter without using the convolution function. Instead, only use the Fourier transform and the inverse Fourier transform. Do you find the same results as shown above? *Hint*: You should.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The more gradual roll-off in the frequency domain corresponds to a more localized impact in the time domain. Here again we are forced to trade desirable features in the time and frequency domains. In the Hanning filter, we forsake the sharp roll-off of the naive rectangular filter&mdash;a desirable property&mdash;for the more local temporal impact, also a desirable property.\n",
    "\n",
    "Now, having visualized the new filter, let’s apply it to the EEG data. To do so, we follow the same procedure used to filter the EEG data with the naive rectangular filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xf = fft(x)                       # Transform data to frequency domain,\n",
    "xf_filtered_h = xf * hann_filter  # ... apply Hanning filter,\n",
    "xnew_h = ifft(xf_filtered_h).real # ... transform back to time domain,\n",
    "                                  # ... and plot the results.\n",
    "plot(t, xnew,   label=\"Rectangular filtered\")\n",
    "plot(t, xnew_h, label=\"Hanning filtered\")\n",
    "xlabel('Time (s)')\n",
    "ylabel('Voltage (mV)')\n",
    "ylim([-.3, .5])\n",
    "legend()\n",
    "savefig('imgs/6-9b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the first three lines of code above, the EEG data are first transformed to the frequency domain using the Fourier transform. Then the Hanning filter is applied through element-by-element multiplication. Finally, the filtered signal is transformed back to the time domain using the inverse Fourier transform. \n",
    "\n",
    "We can additionally compare the filters by looking at the spectra near 60 Hz:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(faxis[:N//2], 10 * log10(spectrum(x, t)), label='x')\n",
    "plot(faxis[:N//2], 10 * log10(spectrum(xnew, t)), label='rectangle filter')\n",
    "plot(faxis[:N//2], 10 * log10(spectrum(xnew_h, t)), label='hanning filter')\n",
    "xlim([40, 80])\n",
    "xlabel('Freq (Hz)')\n",
    "ylabel('Power (dB)')\n",
    "title('Power spectra')\n",
    "legend()\n",
    "savefig('imgs/6-9a')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Compare the results of filtering the EEG data using the naive rectangular filter and the Hanning filter. How do the filters produce similar, and different, results?\n",
    "\n",
    "**A.** Comparison of the resulting spectra shows a sharper and deeper decrease near the 60 Hz peak for the naive rectangular filtered EEG data. In this way, the naive rectangular filter appears to far outperform the Hanning filter; the stop-band of the naive rectangular filter is more focused on eliminating the 60 Hz signal we’d like to remove. The Hanning filter is broader and reduces frequency components extending ±10 Hz around the 60 Hz peak.\n",
    "\n",
    "However, in the time domain, the Hanning filter is far superior. The example shown above illustrates the long-range temporal effects imposed by the naive rectangular filter. Near a brief large discharge in the (unfiltered) EEG data, both filters introduce rhythmic activity for an interval of time. For the Hanning filtered data, these oscillations are a bit larger. For the naive rectangular filtered data, these oscillations persist for a much longer duration; notice that small-amplitude (60 Hz) oscillations appear from time 0 s to time 0.4 s.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having filtered the EEG data in two ways and analyzed the results, we may now make an important conclusion: the naive rectangular filter is a poor choice. Although this filter performs admirably in the frequency domain, the results in the time domain are unacceptable. The naive rectangular filter may confound our understanding of the EEG signal through incorporation of new, long-duration temporal effects in the filtered signal. These results suggest the Hanning filter is a better choice. **However, we do not recommend using this filter.** Instead, we recommend the much safer choice of using filters designed in preexisting software functions. We describe one example of this approach in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "<a id=\"advanced-filters\"></a>\n",
    "## More Sophisticated Filtering\n",
    "\n",
    "In the previous section, we designed two filters. To do so, we started in the frequency domain and applied concepts developed in previous notebooks when studying the spectrum (notebooks <a href=\"03\" rel=\"local\">3</a> and <a href=\"04\" rel=\"local\">4</a>). We undertook this initial approach for one purpose: to build intuition. Developing such intuition is critical; without it, filtering would be hard to understand. However, in practice, we do not recommend the use of the naive rectangular filter or the Hanning filter. This point is so important, we further emphasize it.\n",
    "\n",
    "<div class=\"warning\">\n",
    "\n",
    "Do *not* use the naive rectangular filter or the Hanning filter on your data.\n",
    "\n",
    "</div>\n",
    "\n",
    "Instead, we recommend using preexisting filter design methods provided for Python or other software. In this section, we illustrate the implementation and application of one such method. We continue to use the visualization techniques developed in the previous section to analyze the time and frequency domain representations of the implemented filter. We then apply the filter to the EEG data and examine the results.\n",
    "\n",
    "## The Finite Impulse Response (FIR) Filter: An Example.\n",
    "\n",
    "The most common category of filter applied in neuroscience applications is the finite impulse response (FIR) filter. The name for this approach is actually quite informative. In the previous section, we defined the impulse response; it represents the response of the filter to a signal composed of only a single impulse. “Finite impulse response” indicates that the impulse response consists of only a finite number of nonzero terms. The naive rectangular filter was an example of an infinite impulse response; to represent the naive rectangular filter in the time domain requires an infinite number of terms.<sup><abbr title=\"In practice, all digital filters are finite. We have only a finite amount of computer memory in which to store the filter. In theory, the impulse response of the naive rectangular filter decays to zero as time approaches infinity and therefore contains nonzero contributions for an infinite number of terms.\">note</abbr></sup> We found that such a broad response in the time domain produces unwanted temporal effects in the filtered signal. Here, we instead implement a filter with only a finite number of nonzero terms in the impulse response.\n",
    "\n",
    "Before using packaged routines to create a FIR filter, we might consider how to design our own. A straightforward approach would be to start with an existing filter we developed (e.g., either the naive rectangular filter or the Hanning filter) and truncate the number of terms in the impulse response. By doing so, we would necessarily create a finite impulse response function; all terms beyond a chosen time point would be set to zero. We would therefore eliminate contributions to the filtered signal from inputs far into the past or future. That’s the right idea, but we do not pursue this approach. Instead, we use packaged functions. In this way, we leverage the expertise already inherent in these preexisting filter design approaches.\n",
    "\n",
    "We focus specifically on the application of a lowpass FIR filter to the EEG data. We use the `firwin()` command in from the <a href=\"https://docs.scipy.org/doc/scipy/reference/signal.html\" rel=\"external\">SciPy Signal module</a> to design this filter and then apply it using the convolution function we defined earlier. We then visualize the filter and impulse response in the time and frequency domains. Let’s import the module, define useful parameters, and then design the filter:\n",
    "<a id=\"fig:10a\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100                                        # Define the filter order.\n",
    "Wn = 30 / fNQ                                  # Define the cutoff frequency,\n",
    "b = firwin(n, Wn)                              # ... build the lowpass filter,\n",
    "bz = pad(b, [N - n, 0], 'constant')            # ... amend the filter with leading zeros,\n",
    "impulse_response = convolution(impulse, bz)    # ... and apply it to the impulse.\n",
    "\n",
    "plot(lag_axis, impulse, label='impulse')\n",
    "plot(lag_axis, impulse_response, label='impulse response')\n",
    "legend()\n",
    "ylim([-.02, .08])\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before computing the convolution, we create an augmented vector (variable `bz`). This new vector consists of leading zeros, followed by the filter (variable `b`). The augmented vector has the same length (`N`) as the impulse signal (variable `impulse`), and therefore we can compute the element-by-element multiplication of these two vectors in the same way as we did for the naive rectangular and Hanning filters. Note that the nonzero values of the filter appear at the end of the augmented vector `bz`. To compute the convolution, we shift these nonzero values over the entire length of the augmented vector, and at each shift multiply element by element the two vectors and sum their product.\n",
    "\n",
    "Visual inspection reveals the relation between the original impulse and the filtered impulse following application of the FIR filter. We notice an important difference between the impulse response of the FIR filter and the impulse responses of the naive rectangular and Hanning filters. For the FIR filter, the peak impulse response *follows* the impulse. The reason for this delay is that the FIR filter is *causal*; to compute the convolution at any time requires only past and current values of the input signal. The naive rectangular and Hanning filters required both past and future values of the input signal. Those filters were noncausal.\n",
    "\n",
    "To further explore this idea, let’s examine in more detail the computation of the FIR filter. Notice that to design the filter we call the `firwin()` with two inputs. The first input specifies the filter order, which corresponds to the number of nonzero terms in the filter. We specify a filter order of `n=100`. We next specify the upper frequency for the lowpass filter, which we set to 30 Hz. Notice that the frequency is specified as a fraction of the Nyquist frequency. In this case, we implement a lowpass filter; this filter will pass frequencies below 30 Hz and stop frequencies above 30 Hz. We choose a lowpass filter in this case for physiological reasons; scalp EEG data are often corrupted by muscle artifacts at frequencies above 20–30 Hz. Therefore, in an attempt to better isolate true brain signals and extract an evoked response, we apply a lowpass filter to the EEG data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"python-note\">\n",
    "    \n",
    "**_Note_**: If we had wanted to make a highpass filter, we could have indicated this with additional arguments to `firwin()`; use `firwin?` to read the documentation.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To examine this filter, let’s break down what it does and visualize it in the time and frequency domains. In the time domain, we have already computed the impulse response using the convolution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(arange(0, N) * dt, impulse, label='impulse')                          # Plot the original impulse,\n",
    "plot(arange(0, N) * dt, impulse_response, lw=3, label=\"impulse response\")  # ... and the impulse response.\n",
    "ylim([-.02, .08])                                                          # ... with axes labeled\n",
    "legend()\n",
    "savefig('imgs/6-10a')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's examine this computation closely to understand why there is a lag. To compute the FIR filter, we first constructed the augmented filter vector. To align the filter peak with the impulse requires that we (circularly) shift the augmented filter vector. In this example, the peak in the augmented filter vector (`bz`) occurs at index $N - n/2$, or equivalently, at time $(N - n/2) \\cdot dt$ = 0.55 s, where $N$ is the length of the EEG data, and $n$ is the filter order. We must therefore (circularly) shift the augmented filter vector by $N/2 + n/2$, or equivalently, $(N/2 + n/2) \\cdot dt$ = 0.55 s, to align it with the peak of the impulse (which occurs at index $N/2$, or equivalently, at time $N/2 \\cdot dt$ = 0.5 s). The largest value in the resulting convolution therefore occurs at an index $n/2$ (or equivalently, 0.05 s) past the impulse in the original signal. The delay between the impulse and impulse response in the plot above corresponds to $n/2$ indices, or 0.05 s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** What are the implications of the delay induced by the FIR filter? How might this delay impact subsequent analysis?\n",
    "\n",
    "**A.** We consider this question in more detail later in this module.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may also examine the filter in the frequency domain. To do so, we compute and plot the *magnitude response*:\n",
    "<a id=\"fig:10b\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bf = fft(b, N);                 # Transform filter to frequency domain and compute the response\n",
    "Mb = bf * bf.conj();            # ...and compute the magnitude response.\n",
    "df = 1 / (N * dt)               # Define the frequency resolution,\n",
    "faxis = fftfreq(N, dt);         # ...create frequency axis,\n",
    "sort_order = argsort(faxis)     # ...with axes sorted,\n",
    "plot(faxis[sort_order], Mb.real[sort_order])   # ...plot magnitude response.\n",
    "xlim([-50, 50])\n",
    "xlabel('Frequency (Hz)')\n",
    "ylabel('Magnitude')\n",
    "savefig('imgs/6-10b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We take the Fourier transform of the filter, with zero padding (see <a href=\"04\" rel=\"local\">notebook 4</a>) to match the size of the EEG data, and compute the product of the Fourier transform of the filter and its complex conjugate. We then define the frequency axis, and plot the sorted frequency axis to avoid any unwanted lines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "\n",
    "**Q.** Describe the behavior of the FIR filter in the frequency domain. What frequencies are passed? What frequencies are stopped?\n",
    "\n",
    "**A.** Inspection of the magnitude response shows that frequencies between approximately &plusmn;30 Hz are passed; within this interval, the magnitude response of the filter is above zero. Beyond this interval, the magnitude response decreases to zero. Frequencies greater than 30 Hz or less than -30 Hz are removed in the filtered signal.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having analyzed the filter through inspection of its impulse response and magnitude response, let’s now apply this filter to the EEG data:\n",
    "<a id=\"fig:11a\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xnew_fir_conv = convolution(x, bz)                 # Apply the FIR filter to the data.\n",
    "plot(t, x, label='x')                              # Plot the data,\n",
    "plot(t, xnew_fir_conv, lw=4, label='x filtered')   # ... and the filtered data,\n",
    "legend()\n",
    "xlabel('Time (s)')                                 # ... with axes labeled.\n",
    "ylabel('Voltage (mV)')\n",
    "ylim(ymax=2)\n",
    "savefig('imgs/6-11a')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspection of the resulting filtered signal reveals important features of the new time series. Perhaps the most prominent change is the large reduction in the 60 Hz electrical noise. Without the contamination of this noise, we now observe a transient oscillatory event near 0.5 s. As expected, the spectrum is now dominated by low-frequency activity, namely, rhythms below 30 Hz: \n",
    "<a id=\"fig:11b\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(faxis[:N // 2], 10 * log10(spectrum(x, t)), label='x') # Spectrum of data.\n",
    "plot(faxis[:N // 2], 10 * log10(spectrum(xnew_fir_conv, t)) # Spectrum of filtered data.\n",
    "     , label='x filtered')\n",
    "xlim([0, 100])\n",
    "ylim([-80, 0])\n",
    "xlabel('Freq (Hz)')\n",
    "ylabel('Power (dB)')\n",
    "legend()\n",
    "savefig('imgs/6-11b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's compare the filtered signal using the different filtering methods discussed:\n",
    "<a id=\"fig:11c\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(t, xnew,     label='rectangular filter')         # Plot the results using the rectangular filter, \n",
    "plot(t, xnew_h,   label='Hanning filter')             # ... the Hanning filter,\n",
    "plot(t, xnew_fir_conv, label='lowpass FIR filter')    # ... and the lowpass FIR.\n",
    "ylim([-.3, .4])                                       # Narrow the y axis\n",
    "legend()                                              # Label each line\n",
    "xlabel('Time (s)')                                    # Label the axes\n",
    "ylabel('Voltage (mV)')\n",
    "savefig('imgs/6-11c')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The lowpass filter alters the sharp, brief discharge in the original EEG signal (near 0.2 s) in two important ways. First, we directly observe the temporal shift introduced by the FIR filter; the peak in the filtered signal follows the large voltage deviation in the original signal by 0.05 s<a class=\"sup\" href=\"#fig:11a\">fig<img src=\"imgs/6-11a.png\"></a>). Second, the FIR filter acts to reduce and broaden the large voltage deviation in the original EEG signal, consistent with the impulse response for this filter<a href=\"#fig:10a\" class=\"sup\">fig<img src=\"imgs/6-10a.png\"></a>)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Why would a lowpass filter act to reduce and broaden a brief large discharge in the EEG?\n",
    "\n",
    "**A.** Consider the spectrum of a simpler time series that consists of all zeros except for a single value of 1 at some time index; for example, the simple time series we use to compute the impulse response of a filter. The corresponding spectrum will have nonzero contributions at all frequencies, i.e., representing an impulse requires a combination of sinusoids at many frequencies. Conceptually, an impulse is difficult to represent as a sum of sinusoids. A single sinusoid exists (theoretically) for all time, and we’d somehow like to use these long-duration functions to represent a brief-duration impulse. If we now eliminate some of these sinusoids (e.g., by lowpass filtering the data) we corrupt the representation of the impulse; without these sinusoids, we’re no longer able to accurately represent the sharp, brief impulse in time. Instead, we create an impulse that’s broader and shorter.<span class=\"sup\">fig<img src=\"imgs/6-10a.png\"></span> That’s the best we can do to represent the impulse with the sinusoids we’re given, i.e., the sinusoids with frequency less than 30 Hz. In this way, the lowpass filter acts to smooth the brief large discharge in time.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, inspection of the filtered signal<a href=\"#fig:11c\" class=\"sup\">fig<img src=\"imgs/6-11c.png\"></a> reveals an important advantage over the naive rectangular filter. The small-amplitude 60 Hz activity produced by the naive rectangular filter does not appear in the FIR filtered data. Because the FIR filter acts more locally in time (the impulse response is finite), this filter does not produce the long-lasting temporal effects of the naive rectangular filter. We also note the clear delay induced by the FIR filter compared to the naive rectangular filter.\n",
    "\n",
    "In the preceding code, we applied the FIR filter by computing the convolution. To conclude this section, we introduce a function from the <a href=\"https://docs.scipy.org/doc/scipy/reference/signal.html\" rel=\"external\">SciPy Signal module</a> to apply the FIR filter:\n",
    "\n",
    "    xnew_lfilt = lfilter(b, 1, x)\n",
    "    \n",
    "Here, we call the function `lfilter()` with three arguments. The first argument is the FIR filter we designed at the beginning of this section using the `fir1` command. The second input (a value of 1) is appropriate for the FIR filter we designed here,<sup><abbr title=\"Different values for the second input allow specification of different filter types (e.g., a Butterworth filter) but are not considered here. Consult the documentation for more details.\">note</abbr></sup> and the last input is the EEG signal from trial 1. Let's now plot the signal filtered in this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xnew_lfilt = lfilter(b, 1, x)                                    # Filter the signal using lfilter.\n",
    "plot(t, xnew, label='rectangular filter')                        # Plot the results using the rectangular filter, \n",
    "plot(t, xnew_h, label='Hanning filter')                          # ... the Hanning filter,\n",
    "plot(t, xnew_fir_conv, '--', label='lowpass FIR filter (conv)')  # ... and convolution with the lowpass FIR.\n",
    "plot(t, xnew_lfilt, label='lowpass FIR filter (lfilter)')        # ... and using lfilter with the lowpass FIR.\n",
    "ylim([-.3, .4])                             # Narrow the y axis\n",
    "legend()                                    # Label each line\n",
    "xlabel('Time (s)')                          # Label the axes\n",
    "ylabel('Voltage (mV)')\n",
    "savefig('imgs/6-11c')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We see that after an initial transient, the filtered signal computed using the `lfilter()` function, and the filtered signal computed explicitly using the convolution produce the same result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Apply the FIR filter to the EEG data without using convolution or `lfilter()`. Instead, only use the Fourier transform and inverse Fourier transform. Do you find results consistent with the other two computations? *Hint*: You should.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To summarize, the design and application of a lowpass FIR filter can be performed in two simple steps:\n",
    "\n",
    "    b = firwin(n, Wn)              # Design the lowpass filter, \n",
    "    xnew_lfilt = lfilter(b, 1, x)  # ... and apply it to the signal x\n",
    "    \n",
    "To actually execute these lines of code, we must first define the filter parameters (i.e., the filter order and the cutoff frequency), but the essence of the filtering procedure is captured here. These two lines make the process of filter design and application simple but potentially obfuscate what the filter actually does. We therefore did not immediately implement a filter in this way. Instead, we first examined intuitive ideas for filter design (e.g., the naive rectangular filter and Hanning filter) and visualizations. We expect that these initial examples will provide insight to the packaged routines. In practice, application of these routines is typically the best choice when analyzing your own data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "\n",
    "<a id=\"phase\"></a>\n",
    "## What's Phase Got to Do with It?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We saw in the previous section that the FIR filter (implemented using the `lfilter()` function) introduced a time shift in the resulting signal; this shift appeared in both the <a href=\"#fig:10a\" class=\"fig\">impulse response<span><img src=\"imgs/6-10a.png\"></span></a> and in application to the <a href=\"#fig:11a\" class=\"fig\">EEG signal<span><img src=\"imgs/6-11a.png\"></span></a>. In many applications, we’re interested in the precise timing of neural events. For example, if we’d like to understand the EEG response following a stimulus presentation, we must carefully preserve the timing of EEG features. We discuss in <a href=\"07\" rel=\"local\">notebook 7</a> a specific context in which such timing of features is important to preserve (e.g., cross-frequency coupling). In these contexts and others, shifts in the EEG signal must be either well understood and accounted for, or avoided.\n",
    "\n",
    "To assess how a filter impacts a signal, we develop another visualization technique. Recall that the Fourier transform of a signal consists of both a real and an imaginary component, or equivalently, a magnitude and phase in the complex plane (see, for example, the discussion of phase in <a href=\"05\" rel=\"local\">notebook 5</a>). We have already discussed how to visualize the <a href=\"#fig:10b\" class=\"fig\">magnitude response<span><img src=\"imgs/6-10b.png\"></span></a> of a filter. We now consider a second visualization in the frequency domain: the phase response. The phase response is similar to the magnitude response in that both are frequency domain visualizations of the filter. The primary difference is that the phase response illustrates the impact of the filter on phase at each frequency.\n",
    "\n",
    "Let’s compute the phase response for the lowpass FIR filter. We first construct this filter using the same procedure as above, and then compute and display the phase response. Repeating some commands from previous sections for completeness,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = loadmat('matfiles/EEG-1.mat')    # Load the data,\n",
    "eeg = data['EEG']                       # ... extract the relevant variables,\n",
    "t = data['t'][0]\n",
    "x = eeg[0]                              # ... and analyze the first trial.\n",
    "\n",
    "N = len(x)                              # Define no. of points in trial.\n",
    "dt = t[1] - t[0]                        # Define the sampling interval.\n",
    "fNQ = 1 / dt / 2                        # Define the Nyquist frequency,\n",
    "df = 1 / (N * dt)                       # ... and the frequency resolution,\n",
    "faxis = fftfreq(N, dt);                 # ... create frequency axis,\n",
    "sort_order = argsort(faxis)             # ... with axes sorted.\n",
    "\n",
    "n = 100                                 # Define the filter order,\n",
    "Wn = 30 / fNQ                           # ... specify the cutoff frequency,\n",
    "b = firwin(n, Wn)                       # ... build lowpass filter.\n",
    "bf = fft(b, N)                          # Transform filter to frequency domain,\n",
    "plot(faxis[sort_order], angle(bf[sort_order]))  # ... and plot phase response.\n",
    "\n",
    "xlim([-30, 30])                         # Examine a specific frequency range,\n",
    "xlabel('Frequency (Hz)')                # ... with axes labeled.\n",
    "ylabel('Phase (rad)')\n",
    "savefig('imgs/6-12a')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first load the data and define the frequency axis. We then construct the lowpass FIR filter and plot the phase response versus frequency (with axes sorted to avoid spurious features in the plot). Note that we use the function `angle()` to determine the phase of the vector `bf`. We focus on the passband (from -30 Hz to 30 Hz) because signals outside of this band are greatly reduced by the filter and not relevant in the filtered signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Examine the phase response. How does the phase vary with frequency within the passband (i.e., for frequencies between &plusmn;30 Hz)?\n",
    "\n",
    "**A.** Visual inspection reveals that the phase response varies with frequency. This variation is linear except for discrete jumps occurring at &plusmn;$\\pi$. To make this linear variation clear, we can unwrap the phase:\n",
    "\n",
    "    plot(faxis[sort_order], unwrap(angle(bf[sort_order])))\n",
    "    \n",
    "Notice the application of the `unwrap` function to the angle computed in this line of code. With the phase unwrapped, the smooth and linear variation in the phase response versus frequency becomes clear. The wrapped phase response allows us to identify frequencies at which the filter phase advances the signal (e.g., when the phase response is positive, such as at 15 Hz), when the filter phase delays the signal (e.g., when the phase response is negative, such as at 25 Hz), or when the filter leaves the phase unchanged (e.g., when the phase is zero, such as at 20 Hz).\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(faxis[sort_order], unwrap(angle(bf[sort_order])))  # Plot the unwrapped phase response\n",
    "xlim([-30, 30])                         # Examine a specific frequency range,\n",
    "xlabel('Frequency (Hz)')                # ... with axes labeled.\n",
    "ylabel('Phase (rad)')\n",
    "savefig('imgs/6-12b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analysis of the phase response for the FIR filter shows that, consistent with our observations of the impulse response and filtered EEG data, the FIR filter alters the phase of the original signal. To eliminate this shift introduced by the filter, we apply the same filter twice to the data. First, we apply the FIR filter to the original input signal, just as we did to create the lowpass filtered EEG. This filtering operation introduces a shift (of size n/2 indices, or 0.05 s for our data) in the resulting EEG (e.g., <a href=\"#fig:10a\" class=\"fig\">see above<span><img src=\"imgs/6-10a.png\"></span></a>). Second, we reverse the filtered signal and then apply this same FIR filter to the reversed sequence. The outcome of this second filtering operation is our desired signal: the filtered data without the phase shift.\n",
    "<a id=\"fig:13\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = lfilter(b, 1, x)          # Apply the filter to the EEG data,\n",
    "x1 = flip(x1)                  # ... reverse the sequence,\n",
    "x2 = lfilter(b, 1, x1)         # ... reapply the filter,\n",
    "x2 = flip(x2);                 # ... and reverse the sequence.\n",
    "\n",
    "fig, ax = subplots()           # Plot the results\n",
    "ax.plot(t, x, label='x')\n",
    "ax.plot(t, xnew_fir_conv, lw=5, label='x filtered once')\n",
    "ax.plot(t, x2, lw=5, label='x filtered twice')\n",
    "\n",
    "ylim([-1.5, 2.5])              # Narrow the vertical axis,\n",
    "xlabel('Time (s)')             # ... and label the axes.\n",
    "ylabel('Voltage (mV)')\n",
    "legend()\n",
    "savefig('imgs/6-13')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In these lines of code, we apply the FIR filter using `lfilter()`.The first line of code applies the filter once, and the resulting filtered signal is phase shifted relative to the original EEG. We then reverse the filtered signal. To do so, we redefine the variable `x1` using `flip()` to reverse the sequence. We then filter the reversed sequence, and reverse the result. The resulting double-filtered (and double-reversed) signal no longer exhibits phase distortion relative to the EEG; prominent features in the original EEG signal and the zero-phase filtered signal, such as the large-amplitude discharge, appear better aligned.\n",
    "\n",
    "In general, in neuroscience applications, it’s often useful to remove phase distortion through zero-phase filtering. The <a href=\"https://docs.scipy.org/doc/scipy/reference/signal.html\" rel=\"external\">SciPy Signal module</a> provides a simple function to perform zero-phase filtering,\n",
    "\n",
    "    xnew_filtfilt = filtfilt(b, 1, x)  # Perform zero-phase filtering\n",
    "    \n",
    "The `filtfilt()` function applies the lowpass FIR filter defined by the parameters `b` to the data in the forward and reverse directions, and (ignoring transients at the beginning and end of the signal) matches our explicit approach to zero-phase filtering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(t, filtfilt(b, 1, x), '--', label='x filtfilt')\n",
    "ax.legend()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next section, we apply these commands to complete our analysis of the EEG signal.  \n",
    "\n",
    "Before completing this section, let’s briefly consider an intuitive argument to motivate the procedure for performing zero-phase filtering. Consider the impulse response for the lowpass FIR filter of order $n = 100$ we implemented previously<a href=\"#fig:10a\" class=\"sup\">fig<img src=\"imgs/6-10a.png\"></a>. An impulse at index $k$ will result in a peak at index $k + n/2$ in the filtered signal; the first filtering operation shifts the index of the peak by $n/2$. Now, consider reversing the filtered signal. For concreteness, let’s consider the case where the impulse occurs at index 800 (i.e., k = 800) and the total length of the signal is 2,000 indices. After applying the filter, the peak will occur at index $k + n/2 = 850$. Now, reverse this filtered signal; the peak will then occur at index $2000 - 850 = 1150$. We then filter this new signal, which again shifts the index of the peak by $n/2$; the new peak then occurs at index $1150 + n/2 = 1200$. Finally, we reverse the signal once more; the peak index becomes $2000 - 1200 = 800$. Through this simple example, we gain some intuition for the zero-phase filtering process. By applying the filter twice and reversing the signal appropriately, we maintain the timing of features in the original input signal.\n",
    "\n",
    "Does applying the same filter twice to the signal impacts the results? Yes. Each time we apply the filter, we convolve the signal with the coefficients `b` determined here for the lowpass FIR filter. Each application changes the resulting signal. However, the additional distortion produced by filtering twice is compensated by the elimination of phase distortion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "\n",
    "<a id=\"analysis\"></a>\n",
    "## Analysis of the Filtered EEG Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having introduced some basic filtering concepts, let’s now return to the EEG data. Our primary scientific goal is to determine whether the provided EEG data exhibit an evoked response. Our initial analysis hinted that <a href=\"#fig:3\" class=\"fig\">an evoked response might occur<span><img src=\"imgs/6-3a.png\"></span></a> but was hidden by the large electrical noise—and perhaps other noise—inherent in the EEG data. To reduce this noise, let’s examine the lowpass filtered EEG signal. We choose a lowpass filter to both reduce the 60 Hz electrical noise and reduce other activities associated with nonbrain signals (e.g., muscle artifacts) common in EEG data. In retrospect, the design and application of a lowpass filter with cutoff frequency is now straightforward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = loadmat('matfiles/EEG-1.mat')    # Load the EEG data.\n",
    "eeg = data['EEG']\n",
    "t = data['t'][0]\n",
    "\n",
    "dt = t[1] - t[0]               # Define the sampling interval.\n",
    "fNQ = 1 / dt / 2               # Determine the Nyquist frequency.\n",
    "K = len(eeg)                   # Determine no. of trials.\n",
    "\n",
    "n = 100                        # Define the filter order\n",
    "Wn = 30 / fNQ                  # ... and specify the cutoff frequency,\n",
    "b = firwin(n, Wn)              # ... build lowpass filter.\n",
    "eeg_lo = array([filtfilt(b, 1, eeg[k]) for k in range(K)])  # Zero-phase filter each trial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we use the function `firwin()` to design the filter and the function `filtfilt()` to apply the filter with zero-phase distortion. The design and application of the filter to each trial requires only a few lines of code (including the for-loop). However, we now perform this analysis with a thorough understanding of how the filter behaves; we examined its\n",
    "<a href=\"#fig:10a\" class=\"fig\">impulse response<span><img src=\"imgs/6-10a.png\"></span></a>,\n",
    "<a href=\"#fig:10b\" class=\"fig\">magnitude response<span><img src=\"imgs/6-10b.png\"></span></a>, and <a href=\"#fig:12\" class=\"fig\">phase response<span><img src=\"imgs/6-12a.png\"></span></a>. Let’s now analyze the resulting filtered EEG data by computing the evoked response and average spectrum.\n",
    "<a id=\"fig:14\"></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mn = eeg_lo.mean(0)           # Compute mean of filtered EEG across trials (ERP)\n",
    "sd = eeg_lo.std(0)            # Compute std of filtered EEG data across trials.\n",
    "sdmn = sd / sqrt(K);          # Compute the std of the mean.\n",
    "\n",
    "plot(t, mn)                   # Plot the ERP of the filtered data\n",
    "plot(t, mn + 2 * sdmn, 'r:'); # ... and the confidence intervals,\n",
    "plot(t, mn - 2 * sdmn, 'r:');\n",
    "xlabel('Time [s]')            # ... and label the axes.\n",
    "ylabel('Voltage [ mV]')\n",
    "title('Evoked response')\n",
    "savefig('imgs/6-14a')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eWKZV/sFARERERJqBWqcvrOScexm4Mpnfu3LbCOBO7/1xjdS/+tjr9IVh505YswJWLSesXLb7fuUyWL0CKsp3H1zYLgby3JCePKZXH6ygoIlejohI49P0hSIi+WuK6QsrDWfP2VIA3gGG1ffkTc3atYOSAVAyoNp3LGQrYO3qPUfSVy6DVcsIc1+DHTt2j6RnMtCrT80j6b1LsHZFTfzKRERERKSlySeIPwfc5Zz7HlAGDAS+D7zQCP1qcpYpgOK+UNy3ekgPATashZXLCauWwcrlMaCvXEZ4ez5sfX93SDeDHr1iXXqffsl9CfTuB31KsA6dmviViYiIiEhzlE8Q/wxxSfvZQAFQDvwDuKLhu9W8mBl07xXrxoeM3GNfCAHe37THSPquuvTXXoFNG/a82rVrtz1G0vcoeencVRePioiIiLQRda4Rr+ScywC9gVXe+2yj9Gr/NKsl7sO2LXuMoO+uT18WS2Fydeq8x0g6fUp2B/ZuPRTSRaTRqEZcRCR/+1sjvs8g7pzr6L3fWlsjdT2uiTSrIL4vYcf2eJFozkWjsfRlGaxZCdmczzlF7ZMa9H67pl/cNZLesziW1oiI1JOCuIhI/hr7Ys0VwAF1aGcJ0LO+nWirrKg9lA6C0kHV69LLy2HtqpxwntSnr1hCmDUdynfuLnkpKIz17TkXje66eLS4L1bYrolfmYiIiIjUprYg3sE5d08d2lHSa2BWWLi7hrzKvpDNwvo11eZKZ+UywvzZsH1rzsWjGehZXPM0jL1LsPYdmviViYiIiAjUHsRvrmM7t+xvR6TuLJOBnr2hZ29s2Og99oUQYNOGnOkXcxY1mvESbN6058Wj3XrGWvRddek5o+qdujTp6xIRERFpS/K+WLMFaDE14mkI72+OF45WmeGFlcvjFI25unSNNemVF4xWlrz06Qddu+niUZFWRDXiIiL5a8oFfaQVsM5doPNg7KDB1faF7dtyRtBzRtLfmgtTX4CQ3T2a3r4j9CmpeVGj7r3iqL2IiIiI7JWCuOxi7TvAgINgwEHV69J37oQ1VWd4WQ5liwivTYGK8t0hvbBdDOSVIf2A7tCuHRQVQWERtCvCioritsKiuL1d8rhd++Q+PtZsMCIiItJapR7EnXM/BC4AssBK4DPe+6XOOQN+BZwHbEm2z0ivp22btWsHJQOgZEANF49WxDnRV1afKz3MfQ127KjWXp0LogoKc4J57i3ZloR7qwz67Ypywn3V57XD9gj6VdqqvBUVQWE7ld6IiIhIo6pTEHfOFQB3Ald777c3cB9+5r3/XnKerwD/CVwDnAsMTm7HArcn99LMWKYgTp9Y3BcbccQe+0IIsHNHzm1nDOblyeMdybbyHYQdOcfs3J7c5zx3x444beOur3fA+5thx/Y4Yl++Z3tUVFTra15XRBTmhvt2cS73GsN9TqA/oHvOokwlWi1VRERE9qpOQdx7X+Gc+wBx1LpBee835jzszO6sdAFwj/c+AC8757o75/p575c1dB+k8ZhZDLBF7Ws/toHPHSoq6hDsd8QQX/khIDfMV/kAEaq2sXUL7NwRPxhUtrdlczx3ZSf2ulpqCXTrqZAuIiLShuVTmvIL4AfOuZu89zsbshPOuZuBy4ENwOnJ5v7A4pzDypJt1YK4c+5q4GoA7z3FxcUN2T2ROgvbt1OxYgnly5dQsayMiuVLqFheRsXit6mYPgmyFTkXvHagsKQ/BSX9KSgZEO/7DaCw3wAyvfpgBaqPl6ZTWFio904RkSaWTxD/MlAC/IdzbhU5g37e+0H7eqJzbmLy3Kpu8N4/5L2/AbjBOXcdcC1wEzUPkNZYWeC9nwBMqDxGU3BJqjodAIccAIcM32Nzprwc1q7cvUrqyuWUr1pG+XvvwPTJUJ7z+bZytdScVVJ3TR3Zq2+siRdpQJq+sGmEEODteYRpLxJWryBzvqOmWaxEpGVIpi+st3yC+CfrexLv/Vl1PPQ+4FFiEC8DBubsGwBognBpseJqqaXQp3Tvq6XmXuhaeeHrwjmwLXe1VIsLOuWE892rpfbTaqkijSiEEP9dLpgNmzZgJQOgdFC8RmYv07aGEGDRQsLUFwnTXoS1q6CwEDp0JPvf38LO/BB2wWVYh45N/GpEJG11DuLe++caowPOucHe+wXJww8DbyZfPwxc65y7n3iR5gbVh0trtcdqqUNH7bFv12qpOSG9cvrIMGMybN5YZbXUHjGk77EQU2msT+/ctUlfl0hLF0KA5WWE+bNh/qx4v37N7v2VXxQVQclArHQglA7CSgdB566E16fG8L1qORQUwIgjY+g+Is49EP7vHsLEhwkzJpP55BewUcc0/YsUkdTUOYg759oTZzS5FOjlve+WXMA5xHv/2/3owy3OuaHEC0EXEWdMAfgXcerChcTpC6/Yj3OItFhmFmdjOaA7duiwavvDlvdrDulzZ8Lkp+MxlQd36hJnc+nVG+tRDN17xgWYevSC7vFm7Wu/sFakNQsb1xGmvkSYPwuSkW8gXmA9ZCQMGYkNOTz+m1m2mLD0vV33Yd4sePnZ3f/mMhkYNgY77+PYkcdV+zBsl32BcOypZO+5jeyv/wsbezJ28VVYtx5N+ppFJB11XuLeOfc74sWStwCPee+7O+f6A09470c2Yh/zpSXuRRJhx3ZYtQJWLSWsXJ6UvCyHdavjqN7WLdWf1KkL9OgF3Xti3XvFr3v0il9XPu5ygGZ8aWVUI078APvEg4SXJsaZkHr1icF78Ehs6OGx9KsOv/dh6xZY+h6sXxtDe9dutT9n507C4w8QHvVQ1B676ArspLP170ykmWvKJe4/AhzmvX/fOZcF8N4vScK4iDRDVtQe+g+C/oNqvvp52xZYtxbWryGsWxPD+bo1hMr7skWwcR2EsGf5S2EhdOsJPYqT0fSeu0J6DOzJSLsuKpUWIJS9S3jsAcK0F8Ay2PGnYx+4EOs3sPYn18A6doIa/nq1z+e0a4d96BLCMSeR/fNthHt+S5j2Ipkrvhr/TYlIq5RPEN9R9XjnXG9gTc2Hi0hzZx06Qb9O0K/6iqmVQkUFbFiXjKKv3RXSWb+GsH4tYdFCmLlm1wqqewT2rt2ql7/06IV16cruAYScZ1T9A90ef7Hbx3F77Mv52gwOGRbPLVJFWDCH7GP/C29Mg/YdsbM+jJ11Qaq/L1YygMw3biY8/zjh73eS/f5XyFx+LXbU8an1SUQaTz6lKf8DHAZ8HZgOjAR+CSxMph9sLlSaItLEQgiw5f1qI+p7jLSvX7u71rYpmcHwI7ATzog1unVYXKotaiulKSEEeGNaDOAL58YyqzPHY6ef1+wuZg7Ly8jecSssWhjLVC6+SjOriDQzTVmacj3wU+ANoBOwAPgj8IP6nlxEWgczg85d4q3/gXsfXd+5M4byLZvZ431rjydUebbV4bhqdbTJ4/IdhNdeIUx6mnDHzwkdO2HHnISdcCYcOkz1t61Q2Lpl1zUQYV3ygbDyw+H6NXHqwM2b4gxFl1wdA24zvUDZSgaQ+e5PCA//lfDvBwjzZ5G56hvYwUPS7pqINJA6j4jnSkpSVifLzzc3GhEXkT2EbDZOPTfpKcL0SbBje5zP/YQzYj1wz95pdzF1LXlEPLz3NtkH7oK35sH2rdUP6HLA7rKoHsUweDh2zMlxbv8WIsybRfbOW2H9Wmz8pdh5F2EZrb4rkrb9HRHPpzTlVuBZ4AXv/br6nrAJKIiLyF6FbVsI0ycTJj0F82fF0fRho7ETzsSOPL7Zjo42tpYYxMOmDYQH/0J44Qno3Bkbdyr0LN59TUIyRae1K0q7qw0ibNlMuPd2wtQXYPgYMp//Dta5S9rdEmnTmjKI/xA4BRhLLEt5Lrk9771fVd8ONAIFcRGpk7BqOWHy04RJT8OaldCh4+7SlcOGt6nSlZYUxEN5OeHZRwkP3w/bt2Knnx9HidtAKA0hEF6aSLj3dujdl8yXvxcX7BKRVDRZEK+ULOxzHHA+8Hmgi/e+Of19TEFcRPISsllYMCcpXXkJtm+LK5KecAZ2/BlYrz5pdzEvIZuFbAVUJPfZCqjIud/1deVx5fQaNpK123ak3fVahVkzyP7tDlheBiOOJHPxlXEVyzYmzJ9F9nc/BiDzxeviAkP1aad8J2xY1+J+x0Wai6YcEe8CnAicCpwGDAImAc9572+rbwcagYK4iNRb2LaVMCMpXZn3Rtw4bHQM5EefgLXvkG4HqwhLFhFefDKWK7y/KYbrkM27HetyAPapL2JHndAIvdx/YcVSsn+/E2ZOgT79yLgrYfTYNvVXi6rCyqVkf/NDWLUC+9SXyJx4Zn7Pnz+b7J9vix9qDhmKnfGh+DteqPn/ReqqKYP4TuBd4NfAk977N+t70kamIC4iDSKsXkF4+ZlYurJqeZxr+pgTsOPPhMEjsEwmnX5t3UKY+jzhxYnwznwoKIQx47C+/SBTEB9nMlBQkDyuvM8k+wogk8Eqt4dA5skHKX/rzWY3TV7YuoXw6N8IEx+Bdu2wD12MnTFei0Ulwvubyf7hJzB3Jnbux7ALP1Xr72XYspnwwN2E5x+Pq4eeeBbhledgxRLo1hM77RzslA9iB/Roolch0nI1ZRC/ETgZGA28zu4a8Sne+5317UAjUBAXkQYVQthdujLtpTgzR/ee2OBk+fPBI6B0UKMG8xACLJwbR7+nvRhnfikdFIPzcafVaRn1fenVrRur/t9vCP9+AHqXpDJNXgghzje/YglhxdJ4/8pzsHE9duKZ2Ecux7opHFYVyssJf51AeP7fcNTxZM69CEr6xwW7co8LAWZMIvvXCbBxA3b2BdiHL8Xad4jlTLNfJfv0IzBrBhQWYseeGoN9954pvTKR5i+NGvEC4CjikvdfAgq8983pChkFcRFpNGH7NsKrk+H1aYQFs2NwBOjUJV7gOXhEDOgHHtogf+IPG9bFC0pfmgjLl8RR+XEnYyedDQcPabDSjMqLNcP8WWT/9AtYvwYbfwl27sfjyHkDCps3woqlhBVLYMWy3cF75dL4AaNSuyI4ZCiZj30GO3hwg/ahtQkhEJ56mODv3L26bI/iGMj7DYSSAYTZM2Jpz6BD42qdBx5ac1vLywhP/zPORtOuCLvgMuy08xr890CkNWjKEfGexPrwU4HTgaHEFTaf895fX98ONAIFcRFpEiEEWL0iBvIFcwgL5sQ/7wMUFcHBQ5NgPgIOGVbnco9QUQGzppN98Ul4fSpkszHkn/QB7JgTG6VOPXfWlLBlM+EvvydMeR4OG07ms1/HepfsV/th1XLCM48SXn52zxVWMxko7gt9+2N9S+P87n1LoW//OO93SuU/LVVYvQLee5uwvAyWlcX75WWwbSsUtY+h+szxdQrVYcVSsvf9Aea8CgMPJnPZF7BDhzXBqxBpOZoyiG8BpgDPE0tSJnnva1g5IXUK4iKSmrBxHSyYS1gwOwbzxe/EiyczGRh4CFZZyjJ4RLVykrBiKeGlJwmTnoENa6Frtzhzy4lnY/0GNGq/a5q+MPvys4T7fg8hYJ+4JpbA5DECH0t6ZpN96hF49ZX4X9WRx2GHDMP69oe+pVDcRxcHNrIQQlxhtH17rHPX/J87YxLZ+++IfyU56WzsY5/GuhzQSL0VaVmaMoi3995vr/3I1CmIi0izEbZugbfeJCyYQ1g4G96eD+XJZTUlA2Io7zeQ8NoryQJDGRh1NJmTzoZRxzTZ6o97m0c8rF4RS1UWzsHGnoxd9oVa5+sOO3cSpr5AeOpheO9t6NQFO/WDsbxBq5i2SGHbFsIjf4s/0/4HkrnuZ/oAJUIT14g7504HPgX0B5YA93rvn67vyRuJgriINFth505YtCAG8wVzYOFc2Pp+nLf8xLPiCp89ejV5v/a1oE/IVhAee4DwyF+hW49YqjJ0VPXjNq4jPPtvwnOPwcb10G8gdtZ47NjT2+yKpa1NePVlsr/7b+yDHyVz0WfS7o5I6ppyRPwq4L+BO4BFxHnErwS+573/Y3070AgUxEWkxQjZLKxbDT2KU62HrsvKmuGdBWTv+DmsWoZ98KPYBZ/ACtsR3nuLMPERwtTnobwcRh1D5qzxMPyINj3Pd2uVvee3hBefJPONH9X4gawm4f3NhOcei1MmFhTGWvPDhnTpUP0AABWRSURBVGGHDIPSgVhGF4JKy9SUQXw+8HHv/cycbaOBB7z3zelydgVxEZE81XWJ+7B9G8H/KQaqQYdAh44wfza07xDr2c8Yj5X0b4IeS1rC9m1k/+trUL6DzH/+ep+lSmHlMsLEh+OsPzu2w/AxUNQe3p63+6Ldjp2xi6/Ke0EikeZgf4N4PsWHvYA5VbbNAxpkglHn3DeBnwG9vfernXMG/Ao4D9gCfMZ7P6MhziUiIvVj7Ttgn/oSYdTRZO+5Lc7E8fEr4kV8nZrTTLbSWKx9BzJXfYPsT75N+Mvt8LlvVvvLR1i9Ii4aNH1SXDxq3CnYBy7ABhwc94cAq5YR3ppHeP5xwp9/SyjuU+cRdpHWIp8g/iJwq3PuO977Lc65zsCPicvc7xfn3EDgbOC9nM3nAoOT27HA7cm9iIikzI44jsyYY+OMKppisM2xgwdj4y8lPHgvjB6LHXcaAKF8J+HJhwj/vB8sg53zUeyM87Hue173YGZxqso+pYQx48j++Ftkb7+FzA0/3++pMkVaknzePa8hrqq5wTm3AlgPjAE+3wD9+AXwbSC3TuYC4B7vffDevwx0d871a4BziYhIAzAzhfA2zM79GBw2nHDf7+MI+PxZZP/ra4R/3AMjjyLzX7eR+ejl1UJ4tXY6dSbz5RshBLK//VGcaUikjajzO6j3fpn3/lTgYGA8cLD3/lTv/X4VZDvnPgwsya09T/QHFuc8Lku2iYiISMosU0Dms1+PAfqWb5P92fWwYzuZL3+Pgi9en9dUldanlMw134HlZWT/dCshW9GIPRdpPmotTXHOdQJuBA4HZgA/9t6X5XMS59xEoKa/Nd0AXA98oIZ9NRW+13hlqXPuauBqAO89xcXF+XRPRKTNKyws1Hun5K+4mK1f/A4bb7uFzh+7nM4f/0z9V349+Uy2bFrHpj/eSofH/0HXT32hYfsq0gzVOmuKc+5OYCzwGPHCyWe8919uiJM750YBTxEvxgQYACwFxgE/AJ713v81OXYecJr3flktzWrWFBGRPNV11hSRmoRstkHKlEIIhHt/R3j+8bgA1EX7EexFmkBTzJpyLnCU936Zc+43xCXuGySIe+/fAPpUPnbOvQsck8ya8jBwrXPufuJFmhvqEMJFRESkiTXUtQJmBpd+Hoo6EJ56mDB7BpkrvhZXoBVpheryL6dzZQD23i8GujVul3b5F/A2sBD4I/DFJjqviIiIpMQKC8lcfCWZb9wc689/dh3Zv/8/ws4daXdNpMHVpTRlC3A+u4fdHyTOaLJrGL6ZLXOv0hQRkTypNEWao7BtC+HvdxGe/zd064mNPBKGj8GGj8G69Ui7eyJNUpqyErgz5/GaKo8DcEh9OyAiIiJSE+vQCfvUFwlHnxAX/pk5BSY9FWduKBkABQWwbevu28GDyVx2za6Fg0Sauzovcd+CaERcRCRPGhGXliBks7D4HcKc1whvzY2LBnXsCB06QrsiwqSnYctm7OwLsfGX6EJPaXT7OyKuIC4iIgri0iqEzRsJD9xNePFJ6NWHzCVXwehxWnhKGo2CeHUK4iIieVIQl9YkzJ9F9s+/g+Vl0Lc/dsb52AlnYB06pd01aWUUxKtTEBcRyZOCuLQ2oXwnYfokwlOPwDvzoWMn7KSzsXM+hh3QPe3uSSuhIF6dgriISJ4UxKU1C2/PIzz1CGHqi1BUhJ35YeyDF2KduqTdNWnhFMSrUxAXEcmTgri0BWF5GeGh+wjTXoROXeLo+Bkfwtq3T7tr0kIpiFenIC4ikicFcWlLwntvkX3wL/DGNOjWAzv/Yuzks7HCdml3TVoYBfHqFMRFRPKkIC5tUVgwh+z/3QML5kCvPnHKw2NPVSCXOlMQr05BXEQkTwri0laFEGD2DLL/dy+89xZ074mdOR475RysU+e0uyfNnIJ4dQriIiJ5UhCXtm5XIH/iQZg7Ezp0xI47DRt3Khw6THORS40UxKtTEBcRyZOCuMhu4b23CE8+RJgxCXbsgJ7F2NhT4vSHJf3T7p40Iwri1SmIi4jkSUFcpLqwbSvhtVcIU56HOa9CRQWMOILM6efB6LFYpiDtLkrKFMSrUxAXEcmTgrjIvoUN6wgvPE547nFYvwZ69sZOPSeOkmuBoDZLQbw6BXERkTwpiIvUTaiogJmvkH3mX/Dm61BYiB19Inb6+XDIUMzqncmkBVIQr05BXEQkTwriIvkLyxYTnn2MMPlp2LoFBh6MnX4+Nu5ULRLURiiIV6cgLiKSJwVxkfoL27YSXnmO8MyjsGQRdOqMnXAmdtp5WN/StLsnjUhBvDoFcRGRPCmIi+y/EAIsmEN49l9xxpXk4k478SzsiGOxIo2StzYtPog7574PfA5YlWy63nv/r2TfdcCVQAXwFe/943VoUkFcRCRPCuIiDSte3PkE4YXHYe1q6NgJO+Yk7Pgz4LDhqiVvJVpLEN/svf+fKttHAH8FxgGlwERgiPe+opYmFcRFRPKkIC7SOEI2C/PeIEx+mjBjMmzfBr1LsOPPwI4/HSvum3YXZT/sbxAvbLiuNLgLgPu999uBd5xzC4mhfHK63RIRERGpG8tkYPgYbPgYwieuIcyYRJj0NOHh+wgP3wdDDo+B/OgTsY6d0u6uNLHmEsSvdc5dDkwDvuG9Xwf0B17OOaYs2SYiIiLS4liHjtgJZ8IJZxLWrCS8/GwM5Xf/hnDfH2DU0WTGngyjxmrWlTaiSYK4c24iUFLDrhuA24EfAiG5/znwWWoe5q+xjsY5dzVwNYD3nuLi4gbotYhI21FYWKj3TpGmVFwMQ0cQLv8CO+fNYtuLT7L9pafJzpiMdehI0diTaH/SWbQ/8lisXVHavZVG0iRB3Ht/Vl2Oc879Efhn8rAMGJizewBQY/G3934CMCF5GFTnKCKSH9WIi6SouB9ceDl8+DIy82cTpr7AtumT2PbCk9CxM3bkcdjYk2DYGKywuRQzCOyqEa+31H+azrl+3vtlycOPALOSrx8G7nPO3Uq8WHMwMCWFLoqIiIg0OssUwLDR2LDRhEs/D2/OJEx5gfDqZMKkp6BLV+yoE2MoHzIyHi8tWupBHPipc+4IYtnJu8DnAbz3s51zHpgDlANfqsOMKSIiIiItnhUWwuFHY4cfTdi5A2bPiKH85WcIz/8bunaLI+VHHg/DRmGF7dLustRD6tMXNgJNXygikieVpoi0DGH7NsLr0+DVyfF++9ZYvjL6GOyo42HkUVj7Dml3s81o8fOINwIFcRGRPCmIi7Q8YecOmDOT8OokwmtT4P1NUFQUw/hRx2Ojx2KduqTdzVZNQbw6BXERkTwpiIu0bKGiAubPivXkr74M69dCQQEMHR1D+RHHYt16pN3NVkdBvDoFcRGRPCmIi7QeIZuFdxcQZkwmzJgEq5aDGRw6LAby0eOgpD9m9c6PklAQr05BXEQkTwriIq1TCAGWLIqh/NWXoeyduKNPP2z0OGzMWDhshKZFrCcF8eoUxEVE8qQgLtI2hDWrCK9PJbw+Bd58HcrL48Wehx8FY8Zhhx+NdVZdeV0piFenIC4ikicFcZG2J2zbCnNeI7w+Jc7AsmkDZDJxhHzM2DhiXtI/7W42awri1SmIi4jkSUFcpG0L2Sy8Mz+Ols+cAksWxR19++8K5Rw6TCUsVSiIV6cgLiKSJwVxEckVVq9IQvlUmPcGVJRDh44wfEwsXzn8aKxncdrdTJ2CeHUK4iIieVIQF5G9Cdu2xBKWWTMIs2bAuuS9ov+B2MijYn354BFtcnVPBfHqFMRFRPKkIC4idRFCgKWLCbOmE2ZNhwVz4mh5+w4wbHQcKR91NNarT9pdbRIK4tUpiIuI5ElBXETqI2zbCm++ngTzGbBmZdxRMiAJ5UfB4JFYu6J0O9pIFMSrUxAXEcmTgriI7K8QAixfsjuUz58F5TuhqD0MORwbcQQ24ggoHdRqFhNSEK9OQVxEJE8K4iLS0ML2bTB/FuGN6YS5r8HyJXFHtx7Y8DEw/AhsxBise690O7ofFMSrUxAXEcmTgriINLawZlUM5HNeI8ydCZs3xh39Bu4eLR8yEuvQKd2O5kFBvDoFcRGRPCmIi0hTCtkslL1LmPsaYc5r8aLPnTugoAAOGRqD+fAj4KDBWEFB2t3dKwXx6hTERUTypCAuImkKO3fAwrmEOUkwX/w2hAAdO8PQUdiw0diw0VA6sFnVlyuIV6cgLiKSJwVxEWlOwqaNhDdfh8oR88rZWLp2w4aOSsL5qLjyZ4rBXEG8OgVxEZE8KYiLSHMWVi0nzHsD5r1BePMNWL8m7ujeExsyCoaNigG9d0mTBvNWEcSdc18GrgXKgUe9999Otl8HXAlUAF/x3j9eh+YUxEVE8qQgLiItRQgBVi4jzHsd3nwjBvSN6+POnr1jIB82Chs6GuvVu1H7sr9BvLDhulI/zrnTgQuA0d777c65Psn2EcAlwEigFJjonBviva9Ir7ciIiIikiYzg76lWN9SOOWcZP7yMsKbbxDmvU54YxpMfpoAcYR86CgYejg2eGSzW/Ez9SAOfAG4xXu/HcB7nxQBcQFwf7L9HefcQmAcMDmdboqIiIhIc2NmcQrEfgPh9PPijCxL3yPMe4Pw5uuEGZPgxSdjMO/ZGxs8Ik6TOHhkXAE0xRrz5hDEhwAnO+duBrYB3/TeTwX6Ay/nHFeWbBMRERERqZFlMjDgIGzAQXDmeEK2Apa8R1gwG+bPjheBvvJcDOZdu8Fhw7HKYD7g4CadLrFJgrhzbiJQUsOuG5I+9ACOA8YC3jl3CDXX29RY0O6cuxq4GsB7X1mvIyIiedB7p4i0WgMGwrEnpt2LajJNcRLv/Vne+8NruD1EHOn+h/c+eO+nAFmgONk+MKeZAUCNV2F67yd474/x3h/jnJtODPG6NZObc+6PafdBr7V59bMpz99Y52rodhuivf1pQ++dze+W9r9Tvdbm10+9dzZ8W/vbRvLeWW/NoTTlQeAM4Fnn3BCgCFgNPAzc55y7lXix5mBgSmq9lP3xSNodaEIt5bWm3c+mPH9jnauh222I9tL+uUrDaks/z5byWtPup947G76tVH+mqU9f6JwrAu4EjgB2EGvEn0723QB8ljit4de894/Vob1p3vtjGrHLIiKtjt47RUTyt7/vnamPiHvvdwCf3Mu+m4Gb82xywn53SkSk7dF7p4hI/vbrvTP1EXERERERkbaoSS7WFBERERGRPSmIi4iIiIikQEFcRERERCQFqV+s2dicc52B3xFnZHnWe/+XlLskItLsJQur3QB0895flHZ/RERaAufchcD5QB/gNu/9E/s6vkUGcefcncCHgJXe+8Nztp8D/AooAO7w3t8CfBT4X+/9I865vwEK4iLSJuXz3um9fxu40jn3v+n0VkSkecjzvfNB4EHnXA/gf4B9BvGWWppyF3BO7gbnXAFwG3AuMAK41Dk3grgi5+LksIom7KOISHNzF3V/7xQRkegu8n/vvDHZv08tMoh7758H1lbZPA5Y6L1/O5mb/H7gAqCMGMahhb5eEZGGkOd7p4iIkN97p3POnHM/AR7z3s+ore3WFEz7s3vkG2IA7w/8A/iYc+520l+aVkSkuanxvdM518s593vgSOfcdel0TUSk2dpb7vwycBZwkXPumtoaaZE14nthNWwL3vv3gSuaujMiIi3E3t471wC1/iciItJG7e2989fAr+vaSGsaES8DBuY8HgAsTakvIiIthd47RUTy1yDvna1pRHwqMNg5dzCwBLgE+ES6XRIRafb03ikikr8Gee+0EEJDd6zROef+CpwGFAMrgJu8939yzp0H/JI4jcyd3vub0+uliEjzovdOEZH8NeZ7Z4sM4iIiIiIiLV1rqhEXEREREWkxFMRFRERERFKgIC4iIiIikgIFcRERERGRFCiIi4iIiIikQEFcRERERCQFrWlBHxERaUaccwcB7wDvA//hvZ/QAG2+RVzNznvvP7m/7YmIpElBXESkgTnn3gX6AhU5m4d479vq0vHdvfflAM6504B7vfcDcg9wzj2bbL9jXw157w91zn0fOKxxuioi0nQUxEVEGsd47/3EfR3gnCusDKgiItL2KIiLiDSRnFKNq4CbgHeBU5xzxwG3AiOARcBXvffPJs85GLgLOAp4GZhHHGH+ZE2jy8lo/FXe+4nOuQzwbeBzQHfgKeAa7/3anL58Bvgh0An4ReUSzc65AuA7wJVAH2A+cCHwXWCb9/4bOed8BHjKe//LBvo+PQKcnrOpE/BZ7/1dDdG+iEhzoYs1RUSa3qnAcOCDzrn+wKPAj4CewDeBB5xzvZNj7wOmA8XEwPzpPM7zFWJ4PhUoBdYBt1U55iRgKHAm8J/OueHJ9v8ALgXOAw4APgtsAe4GLk1CPs654uS5f82jX/vkvR/vve/ive8CXAQsJ36IEBFpVTQiLiLSOB50zlWWnTzrvb8wZ9/3vffvAzjnPgn8y3v/r2Tfk865acB5zrlngLHAWd777cDzyWhxXX0euNZ7X5ac6/vAe865T+Uc8wPv/VZgpnNuJjAGmEsctf+2935ectzM5H6Nc24DMXw/CVySvL4VefSr1Dm3vsq2LsC9uRucc0OAe4CPee8X59G+iEiLoCAuItI4LtxHjXhuqDwQ+LhzbnzOtnbAMySj2JWhPbGIOGtIXRwI/J9zLpuzrYJ4IWml5TlfbyEGYpJzvLWXdu8GPkkM4p8EflXH/lRaupeLNXMfdwMeAr7nvX8hz/ZFRFoEBXERkaYXcr5eDPzZe/+5qgc55w4EejjnOueE8UE5z3+fWD9deXwB0DunicXE2uqXamj7oFr6uBg4FJhVw757gVnOuTHEEpsHa2krL0nZy33AM977PzRk2yIizYmCuIhIuu4FpjrnPghMJI6GHwcs9N4vSspUfuCcux4YB4wHHk6eOx/o4Jw7H3gCuB5on9P274GbnXOfTtrqDZzgvX+oDv26A/ihc24OsBAYBSzx3q/x3pc556YCfwYeSEpbGtLNQGfgqw3crohIs6KLNUVEUpTUPl9ADNGriCPR32L3+/MngGOBtcSZVu7Jee4G4IvE0LyEOEJeltP8r4ih/Qnn3CbirCvH1rFrtwKeGPA3An8COubsv5sYzv9cx/bycSnxw8g659zm5HZZI5xHRCRVFkKo/SgREWkWKhezSXtVSefcKcTR/IO899m9HHMgcbrFbcC3vPd/bIDzzgP6E1fW/Oz+ticikiaVpoiISF6cc+2IZSN37C2EA3jvFwEdGvLc3vuhDdmeiEiaVJoiIiJ1lswzvh7oBzTIAj4iIm2VSlNERERERFKgEXERERERkRQoiIuIiIiIpEBBXEREREQkBQriIiIiIiIpUBAXEREREUmBgriIiIiISAr+P/0btIPuMzsEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def spectrum(x, t, hann=True):\n",
    "    '''\n",
    "    Define a function that computes the power spectrum \n",
    "    for any given trial data (x) and corresponding sample time (t).\n",
    "    '''\n",
    "    dt = t[1] - t[0]\n",
    "    T = t[-1]\n",
    "    xh = hanning(len(x)) * (x - x.mean()) if hann else x - x.mean()\n",
    "    xf = rfft(xh)[:-1]\n",
    "    Sxx = 2 * dt ** 2 / T * (xf * xf.conj())\n",
    "    return Sxx.real\n",
    "\n",
    "N = len(t)                             # Define the number of time points per trial.\n",
    "faxis = fftfreq(N, dt)[:N // 2]        # Define the positive frequency axis,\n",
    "Sxx = [spectrum(trial, t, False) for trial in eeg_lo]  # Compute the spectrum for each trial.\n",
    "Sxxmn = array(Sxx).mean(0)             # Convert the result into an array and compute the mean.\n",
    "semilogx(faxis, 10 * log10(Sxxmn))     # Plot the result in decibels vs frequency,\n",
    "xlim([df, 100])                        # ... in limited frequency range,\n",
    "ylim([-60, 0])                         # ... and a limited power range,\n",
    "xlabel('Frequency [Hz]')               # ... with axes labeled.\n",
    "ylabel('Power [dB]')\n",
    "title('Trial averaged spectrum')\n",
    "savefig('imgs/6-14b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"question\">\n",
    "    \n",
    "**Q.** Compare the <a href=\"#fig:3\" class=\"fig\">evoked response<span><img src=\"imgs/6-3a.png\"></span></a> and <a href=\"#fig:3\" class=\"fig\">spectrum<span><img src=\"imgs/6-3b.png\"></span></a> of the original EEG data to the evoked response and spectrum of the filtered data. What features are similar? What features differ?\n",
    "\n",
    "**A.** To compute the evoked response and average spectrum, we apply the same procedures utilized for the original data (see code [above](#evoked-response)). We now find that between approximately 0.4 s and 0.6 s, the filtered EEG signal exhibits a signifiant ERP; the 95% confidence intervals of the ERP now exclude zero in this range. We are therefore happy to report to our collaborator evidence for a significant ERP in the filtered EEG data. We also note the reduced impact in the ERP of the large, brief discharges that appear in individual trials. In the original EEG data, each discharge from an individual trial was so large that the <a href=\"#fig:3\" class=\"fig\">impact on the ERP was dramatic<span><img src=\"imgs/6-3a.png\"></span></a> (e.g., consider times near 0.2 s and near 0.8 s). In the filtered EEG data, these discharges have been smoothed, and their impact greatly reduced in the ERP.\n",
    "\n",
    "Inspection of the average spectrum for the filtered EEG data reveals power at low frequencies and perhaps a small peak at 15–25 Hz, as observed in the unfiltered EEG data. Again, we note that the approximately 15–25 Hz peak in the spectrum is consistent with the period of the transient rhythmic discharge in the ERP. The filtered data exhibit much less power spectral density at higher frequencies compared to the original EEG; this is what we expect following application of the lowpass filter.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Back to Top](#top)\n",
    "\n",
    "<a id=\"summary\"></a>\n",
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We began this notebook with visual analysis of the single-trial data and computation of an ERP and trial-averaged spectrum. The spectrum revealed a large peak at 60 Hz, consistent with visual inspection of the single-trial data. The ERP showed some suggestive evidence for an evoked response; however, we did not find a significant effect. We made an initial conjecture that an interesting evoked response might occur in the data but was hidden by the large-amplitude 60 Hz noise.\n",
    "\n",
    "To isolate the evoked response, we then focused on reducing the 60 Hz activity in the signal. We introduced the notion of filtering. We put forward two naive approaches, the naive rectangular filter, and the naive Hanning filter and developed these approaches in great detail. We defined the notion of an impulse response and examined how filtering may be equivalently applied in the frequency domain (through multiplication) or in the time domain (through convolution). Through these example filters, we observed the trade-offs that occur in the time and frequency domains. In particular, we observed that the sharp edge in the frequency domain of the naive rectangular filter created long-lasting effects in the time domain, acting to distort the original signal.\n",
    "\n",
    "We then discussed the application of a finite impulse response (FIR) filter to the data. We showed how this filter may be easily defined and applied in Python using packaged functions. We discussed procedures to visualize a filter’s behavior, including the magnitude response and the phase response. Finally, we discussed the importance of zero-phase filtering.\n",
    "\n",
    "We concluded by reanalyzing the EEG data. To do so, we first lowpass filtered the data and then computed the evoked response and trial-averaged spectrum. After filtering, we found a significant evoked response in the data. Consistent with our initial conjecture, the evoked response was hidden by the high-amplitude 60 Hz noise present in the original signal. Upon filtering to remove this noise, the evoked response became clear.\n",
    "\n",
    "The design and application of filters is an enormous and rich field of study. The goal of this notebook is not a thorough discussion of filtering. Instead, we introduced only a handful of filtering concepts that motivate a basic understanding of filtering. These concepts extend directly from ideas developed to compute the spectrum in notebooks <a href=\"03\" rel=\"local\">3</a> and <a href=\"04\" rel=\"local\">4</a>. Through tools such as the Fourier transform and convolution, we are able to visualize and apply filters in the frequency and time domains. These same tools apply and provide context for alternative approaches to filtering. For further details in the design and application of filters see [<a href=\"https://doi.org/10.1017/CBO9780511622762\" rel=\"external\">Percival & Walden, 1998</a>, <a href=\"https://buprimo.hosted.exlibrisgroup.com/permalink/f/1du03mk/ALMA_BOSU121668583370001161\" rel=\"external\">Priestley, 1981</a>]. We apply filters in <a href=\"07\" rel=\"local\">notebook 7</a> to assess cross-frequency coupling in neural field data.\n",
    "\n",
    "[Back to Top](#top)"
   ]
  },
  {
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    "<a id=\"donate\"></a>\n",
    "## Donate\n",
    "If you enjoy Case-Studies-Python, and would like to share your enjoyment with us, sponsor our coffee consuption <a href=\"https://www.paypal.com/donate/?hosted_button_id=DL8P5ZGS9962U\">here</a>."
   ]
  }
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