{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fourier transform\n", "\n", "> Marcos Duarte \n", "> Laboratory of Biomechanics and Motor Control ([http://demotu.org/](http://demotu.org/)) \n", "> Federal University of ABC, Brazil" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In continuation to the notebook about [Fourier series](http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/FourierSeries.ipynb), the [Fourier transform](http://en.wikipedia.org/wiki/Fourier_transform) is a mathematical transformation to transform functions between time (or spatial) domain and frequency domain. The process of transforming from time to frequency domain is called Fourier analysis, the inverse is the Fourier synthesis.\n", "\n", "The Fourier transform of a continuous function $x(t)$ is by definition:\n", "\n", "$$ X(f) = \\int_{-\\infty}^{\\infty} x(t)\\:\\mathrm{e}^{-i2\\pi ft} \\:\\mathrm{d}t $$\n", "\n", "And the inverse Fourier transform is:\n", "\n", "$$ x(t) = \\int_{-\\infty}^{\\infty} X(f)\\:\\mathrm{e}^{\\:i2\\pi tf} \\:\\mathrm{d}f $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete Fourier transform\n", "\n", "For discrete data, $x$ with length $N$, its Discrete Fourier Transform (DFT) is another data $X$, also with length $N$ and elements:\n", " \n", "$$ X[k] = \\sum_{n=0}^{N-1} x[n] \\mathrm{e}^{-i2\\pi kn/N} \\;,\\quad 0 \\leq k \\leq N-1 $$\n", "\n", "The Inverse Discrete Fourier Transform (IDFT) inverts this operation and gives back the original data $x$:\n", "\n", "$$ x[n] = \\frac{1}{N} \\sum_{k=0}^{N-1} X[k] \\mathrm{e}^{i2\\pi kn/N} \\;,\\quad 0 \\leq n \\leq N-1 $$\n", "\n", "The relationship between the DFT and the Fourier coefficients $a$ and $b$ in\n", "\n", "$$ x[n] = a_0 + \\sum_{k=1}^{N-1} a[k]\\cos\\left(\\frac{2\\pi kt[n]}{Ndt}\\right)+b[k]\\sin\\left(\\frac{2\\pi kt[n]}{Ndt}\\right) \\;,\\quad 0 \\leq n \\leq N-1 $$\n", "\n", "is:\n", "\n", "$$ \\begin{array}{l}\n", "a_0 = X[0]/N \\\\\\\n", "\\\\\\\n", "a[k] = \\;\\; \\text{Real}(X[k+1])/N \\\\\\\n", "\\\\\\\n", "b[k] = -\\text{Imag}(X[k+1])/N\n", "\\end{array} $$\n", "\n", "Where $x$ is a length $N$ discrete signal sampled at times $t$ with spacing $dt$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fast Fourier Transform (FFT)\n", "\n", "The [FFT](http://en.wikipedia.org/wiki/Fast_Fourier_transform) is a fast algorithm to compute the DFT. Let's see how to use the FFT algorithm from `scipy.fftpack`." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import sys\n", "sys.path.insert(1, r'./../functions')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A sine wave with amplitude of 2, frequency of 5 Hz, and phase of 45$^o$ sampled at 100 Hz:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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PmHWXvZpfU2Dy5gpbKm8u49CBxTaQesPGPFJwAA3JR/kjO7Ttrn2kXmZQAZ6I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\nFifoKYGVC58qr3nHmkdWfnSg2lzh8rpKOqa+CuTSXJi/DH2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = 2 # amplitude\n", "freq = 5 # Hz\n", "phase = np.pi/4 # radians (45 degrees)\n", "fs = 100\n", "dt = 1 / fs\n", "time = np.arange(0, 500) / fs\n", "x = A * np.sin(2 * np.pi * freq * time + phase) + 1\n", "x = np.asarray(x)\n", "N = x.shape[0]\n", "t = np.arange(0, N) / fs\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(9, 3))\n", "ax.plot(time, x, linewidth=2)\n", "ax.set_xlabel('Time [s]')\n", "ax.set_ylabel('Amplitude')\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Its FFT is simply:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from scipy.fftpack import fft, fftfreq, fftshift\n", "\n", "X = fft(x, N) # FFT\n", "freqs = fftfreq(N, dt) # frequency values\n", "amp = np.abs(X)/N # amplitude\n", "phase = -np.imag(X)/N * 180/np.pi # phase" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, figsize=(9, 5), sharex=True)\n", "ax[0].plot(freqs, amp)\n", "ax[1].plot(freqs, phase)\n", "ax[0].set_ylabel('Amplitude')\n", "ax[1].set_xlabel('Frequency [Hz]')\n", "ax[1].set_ylabel('Phase $[\\;^o]$')\n", "ax[0].set_ylim(-.01, 1.1)\n", "ax[1].set_xlim(-50, 50)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For real signals, the FFT values are the same for negative and positive frequencies and the phase is negated if the signal is odd and the same if the signal is even. Because that, we usually don't care about the negative frequencies and plot only the FFT for the positive frequencies:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "freqs2 = freqs[:int(np.floor(N/2))]\n", "amp2 = amp[:int(np.floor(N/2))] # amplitude\n", "amp2[1:] = 2*amp2[1:] # DC component appears only once\n", "phase2 = phase[:int(np.floor(N/2))] # phase\n", "\n", "fig, ax = plt.subplots(2, 1, figsize=(9, 5), sharex=True)\n", "ax[0].plot(freqs2, amp2)\n", "ax[1].plot(freqs2, phase2)\n", "ax[0].set_ylabel('Amplitude')\n", "ax[1].set_xlabel('Frequency [Hz]')\n", "ax[1].set_ylabel('Phase [$^o$]')\n", "ax[0].set_ylim(-.01, 2.1)\n", "ax[1].set_xlim(-.1, 50)\n", "ax[1].set_ylim(-.2, 50)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can get back the $x$ data with the FFT synthesis:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from scipy.fftpack import fft\n", "\n", "X = fft(x, N)\n", "\n", "# Fourier coefficients\n", "a = np.zeros(N)\n", "b = np.zeros(N)\n", "a[0] = np.real(X[0]) / N\n", "a[1:N] = +np.real(X[1:N]) / N\n", "b[1:N] = -np.imag(X[1:N]) / N\n", "\n", "# Fourier synthesis based on the Fourier coefficients\n", "y = np.zeros((N, N))\n", "for k in np.arange(0, N):\n", " w = 2 * np.pi * k / (N * dt)\n", " y[:, k] = a[k] * np.cos(w * t) + b[k] * np.sin(w * t)\n", "\n", "xfft = np.sum(y, axis=1)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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/M94XoSAuNqsNSZa6moKNeCJfVyTAldvWsfTv59FYORwWKOsv5mlqwyXE8Zis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\n/wNrnkStWjqGYAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(9, 3))\n", "ax.plot(time, x, linewidth=2, label='Original data')\n", "ax.plot(t, xfft, 'r--', linewidth=2, label='FFT synthesis')\n", "ax.set_xlabel('Time [s]')\n", "ax.set_ylabel('Amplitude')\n", "ax.legend(framealpha=.7)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But employing the function `scipy.fftpack.fft` is simpler:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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/M94XoSAuNqsNSZa6moKNeCJfVyTAldvWsfTv59FYORwWKOsv5mlqwyXE8Zis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SxHfV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AvoqiTND+DdiN8IeiKP8GjgcCwNtCiMPSPG+JRCL5VkgBUCKRSIzxDpBI7hBCTNjdDUKIGmCT\noigPAK8A47+76UkkEknvSAFQIpFIjHElMEVL5vgKNb5vd5wBrBJCrABGAv/8LicokUgkvSEURenv\nOUgkEsn/S4QQFwBTdlUGJuVnt2g/2/Jdz0sikUikBVAikUi+OwLA7G9TCBrIQI0xlEgkku8caQGU\nSCQSiUQi2cuQFkCJRCKRSCSSvQwpAEokEolEIpHsZUgBUCKRSCQSiWQvQwqAEolEIpFIJHsZ/wd4\n0IbC6KhMlAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.fftpack import ifft\n", "\n", "xfft2 = np.real(ifft(X))\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(9, 3))\n", "ax.plot(time, x, linewidth=2, label='Original data')\n", "ax.plot(t, xfft2, 'r--', linewidth=2, label='iFFT synthesis')\n", "ax.set_xlabel('Time [s]')\n", "ax.set_ylabel('Amplitude')\n", "ax.legend(framealpha=.7)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another example:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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P+/ooKSwAjBtHxwULipWZ9FzlfXHdrUOCJ0Imfi4KoC3p8W23UZlJCiCQ/TyT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\nwVIAy6KzkwiV72g93/DhA2iDNCEAtLn4ppvS83clgMOHAz/8Yfm6mUg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "freq = 100.0\n", "t = np.arange(0, 5, .01)\n", "y = 2*np.sin(5*np.pi*2*t) + np.sin(2*np.pi*20*t) + np.random.randn(t.size) \n", "\n", "fig, ax = plt.subplots(1, 1, squeeze=True, figsize=(9, 3))\n", "\n", "ax.set_title('Temporal domain', fontsize=18)\n", "ax.plot(t, y, 'b', linewidth=2)\n", "ax.set_xlabel('Time [s]')\n", "ax.set_ylabel('y')\n", "ax.locator_params(axis = 'both', nbins = 5)\n", "fig.tight_layout()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# frequency content\n", "N = y.size\n", "yfft = fft(y, N)\n", "# Only the positive frequencies\n", "yfft = 2*np.abs(yfft)/N\n", "freqs = fftfreq(N, 1./freq)\n", "freqs = freqs[:int(np.floor(N/2))]\n", "yfft = yfft[:int(np.floor(N/2))]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, squeeze=True, figsize=(9, 3))\n", "ax.set_title('Frequency domain', fontsize=18)\n", "ax.plot(freqs, yfft, 'r', linewidth=2)\n", "ax.set_xlabel('Frequency [Hz]')\n", "ax.set_ylabel('FFT(y)')\n", "ax.locator_params(axis = 'both', nbins = 5)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### FFTW - the Fastest Fourier Transform in the West\n", "\n", "[FFTW](http://www.fftw.org/) is a free collection of fast C routines for computing the DFT. Indeed, FFTW is probably the fastest FFT library in the market and you should use it in case speed is a major concern. To use it in Python, you will need to install FFTW and the Python wrapper around FFTW, [pyfftw](https://pypi.python.org/pypi/pyFFTW)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Power spectral density \n", "\n", "The function `psd.py` (code at the end of this text) estimates power spectral density characteristics using Welch's method. This function is just a wrap of the scipy.signal.welch function with estimation of some frequency characteristics and a plot. The `psd.py` returns power spectral density data, frequency percentiles of the power spectral density (for example, Fpcntile[50] gives the median power frequency in Hz); mean power frequency; maximum power frequency; total power, and plots power spectral density data.\n", "\n", "Let's exemplify the use of `psd.py`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on function psd in module psd:\n", "\n", "psd(x, fs=1.0, window='hanning', nperseg=None, noverlap=None, nfft=None, detrend='constant', show=True, ax=None, scales='linear', xlim=None, units='V')\n", " Estimate power spectral density characteristcs using Welch's method.\n", " \n", " This function is just a wrap of the scipy.signal.welch function with\n", " estimation of some frequency characteristcs and a plot. For completeness,\n", " most of the help from scipy.signal.welch function is pasted here.\n", " \n", " Welch's method [1]_ computes an estimate of the power spectral density\n", " by dividing the data into overlapping segments, computing a modified\n", " periodogram for each segment and averaging the periodograms.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Time series of measurement values\n", " fs : float, optional\n", " Sampling frequency of the `x` time series in units of Hz. Defaults\n", " to 1.0.\n", " window : str or tuple or array_like, optional\n", " Desired window to use. See `get_window` for a list of windows and\n", " required parameters. If `window` is array_like it will be used\n", " directly as the window and its length will be used for nperseg.\n", " Defaults to 'hanning'.\n", " nperseg : int, optional\n", " Length of each segment. Defaults to half of `x` length.\n", " noverlap: int, optional\n", " Number of points to overlap between segments. If None,\n", " ``noverlap = nperseg / 2``. Defaults to None.\n", " nfft : int, optional\n", " Length of the FFT used, if a zero padded FFT is desired. If None,\n", " the FFT length is `nperseg`. Defaults to None.\n", " detrend : str or function, optional\n", " Specifies how to detrend each segment. If `detrend` is a string,\n", " it is passed as the ``type`` argument to `detrend`. If it is a\n", " function, it takes a segment and returns a detrended segment.\n", " Defaults to 'constant'.\n", " show : bool, optional (default = False)\n", " True (1) plots data in a matplotlib figure.\n", " False (0) to not plot.\n", " ax : a matplotlib.axes.Axes instance (default = None)\n", " scales : str, optional\n", " Specifies the type of scale for the plot; default is 'linear' which\n", " makes a plot with linear scaling on both the x and y axis.\n", " Use 'semilogy' to plot with log scaling only on the y axis, 'semilogx'\n", " to plot with log scaling only on the x axis, and 'loglog' to plot with\n", " log scaling on both the x and y axis.\n", " xlim : float, optional\n", " Specifies the limit for the `x` axis; use as [xmin, xmax].\n", " The defaukt is `None` which sets xlim to [0, Fniquist].\n", " units : str, optional\n", " Specifies the units of `x`; default is 'V'.\n", " \n", " Returns\n", " -------\n", " Fpcntile : 1D array\n", " frequency percentiles of the power spectral density\n", " For example, Fpcntile[50] gives the median power frequency in Hz.\n", " mpf : float\n", " Mean power frequency in Hz.\n", " fmax : float\n", " Maximum power frequency in Hz.\n", " Ptotal : float\n", " Total power in `units` squared.\n", " f : 1D array\n", " Array of sample frequencies in Hz.\n", " P : 1D array\n", " Power spectral density or power spectrum of x.\n", " \n", " See Also\n", " --------\n", " scipy.signal.welch\n", " \n", " Notes\n", " -----\n", " An appropriate amount of overlap will depend on the choice of window\n", " and on your requirements. For the default 'hanning' window an\n", " overlap of 50% is a reasonable trade off between accurately estimating\n", " the signal power, while not over counting any of the data. Narrower\n", " windows may require a larger overlap.\n", " If `noverlap` is 0, this method is equivalent to Bartlett's method [2]_.\n", " \n", " References\n", " ----------\n", " .. [1] P. Welch, \"The use of the fast Fourier transform for the\n", " estimation of power spectra: A method based on time averaging\n", " over short, modified periodograms\", IEEE Trans. Audio\n", " Electroacoust. vol. 15, pp. 70-73, 1967.\n", " .. [2] M.S. Bartlett, \"Periodogram Analysis and Continuous Spectra\",\n", " Biometrika, vol. 37, pp. 1-16, 1950.\n", " \n", " Examples (also from scipy.signal.welch)\n", " --------\n", " #Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by\n", " # 0.001 V**2/Hz of white noise sampled at 10 kHz and calculate the PSD:\n", " >>> from psd import psd\n", " >>> fs = 10e3\n", " >>> N = 1e5\n", " >>> amp = 2*np.sqrt(2)\n", " >>> freq = 1234.0\n", " >>> noise_power = 0.001 * fs / 2\n", " >>> time = np.arange(N) / fs\n", " >>> x = amp*np.sin(2*np.pi*freq*time)\n", " >>> x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)\n", " >>> psd(x, fs=freq);\n", "\n" ] } ], "source": [ "from psd import psd\n", "help(psd)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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EREREDsQkTaMfVh60OwQiIiKy0Idz9yDVQdutMUnTaASLzYmIiAq839Y6p70K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\nyhfDCz3roZrG+1PbgzYUPNy+JmJLF9U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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by\n", "# 0.001 V**2/Hz of white noise sampled at 10 kHz and calculate the PSD:\n", "fs = 10e3\n", "N = 1e5\n", "amp = 2*np.sqrt(2)\n", "freq = 1234.0\n", "noise_power = 0.001 * fs / 2\n", "time = np.arange(N) / fs\n", "x = amp*np.sin(2*np.pi*freq*time)\n", "x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(time, x, linewidth=2)\n", "plt.xlabel('Time [s]')\n", "plt.ylabel('Amplitude');" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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OOWXv9ZdeGkwbN+7d534c112UNJzookWLmD9/Pjt27ODwww9nzJgxzJ8/n+uv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\n2PeqUrZFyx05xvZdwXGzwu9XUE6L/n1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fpcntile, mpf, fmax, Ptotal, f, P = psd(x, fs=freq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Periodogram" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "import scipy\n", "freq = 100.0\n", "t = np.arange(0, 5, .01)\n", "y = 2*np.sin(5*np.pi*2*t) + np.sin(2*np.pi*20*t) + np.random.randn(t.size) \n", "N = y.shape[0]\n", "\n", "from scipy import signal, integrate\n", "fp, Pp = signal.periodogram(y, freq, window='boxcar', nfft=N)\n", "fw, Pw = signal.welch(y, freq, window='hanning', nperseg=N, noverlap=0, nfft=N)\n", "# quick and simple PSD\n", "P = np.abs(scipy.fftpack.fft(y-np.mean(y),N))[:int(np.floor(N/2))]**2/N/freq; P[1:-1]=2*P[1:-1]\n", "fs = np.linspace(0,freq/2,len(P))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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WJaTf9dxzdGSCtXJllAQAhfbv1VfLazcJwXLliFYCO89dnkNTE9ncnj2NSrd2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\nwWABVk1NBFnu/GcPUAjpAKu1N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ozz7dVXx7Vp/vxYPz098TD3xz+OKuQTJsT4xsb8/V1n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\nUCD/HyRi3BjUJK+VAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1,ax2,ax3) = plt.subplots(3, 1, squeeze=True, figsize=(12, 8))\n", "ax1.set_title('Temporal domain', fontsize=18);\n", "ax1.plot(t, y, 'b', linewidth=2)\n", "ax1.set_xlabel('Time [s]'); ax1.set_ylabel('y [V]'); \n", "ax1.locator_params(axis = 'both', nbins = 5);\n", "ax2.set_title('Frequency domain', fontsize=18);\n", "ax2.plot(fp, Pp,'r', linewidth=2)\n", "ax2.set_xlabel('Frequency [Hz]'); ax2.set_ylabel('PSD(y) $[V^2/Hz]$');\n", "ax2.locator_params(axis = 'both', nbins = 5);\n", "ax3.set_title('Frequency domain', fontsize=18);\n", "ax3.plot(fw, Pw,'r', linewidth=2)\n", "ax3.set_xlabel('Frequency [Hz]'); ax3.set_ylabel('PSD(y) $[V^2/Hz]$');\n", "ax3.locator_params(axis = 'both', nbins = 5);\n", "fig.tight_layout()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "F, P = signal.welch(y, fs=freq, window='hanning', nperseg=N/2, noverlap=N/4, nfft=N/2)\n", "A = integrate.cumtrapz(P, F)\n", "fm = np.trapz(F * P, F)/np.trapz(P, F)\n", "f50 = F[np.nonzero(A >= 0.5*A[-1])[0][0]]\n", "f95 = F[np.nonzero(A >= .95*A[-1])[0][0]]\n", "fmax = F[np.argmax(P)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ F_{mean} = \\frac{ \\sum_{i=1}^{N} F_i*P_i }{ \\sum_{i=1}^{N} P_i } $$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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69OHnn38GYOHChfTo0YPOnTvTr18/9u/fD8CkSZMYPXo0ffv2pUWLFrz88sun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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from psd import psd\n", "fp, mf, fmax, Ptot, F, P = psd(y, fs=freq, scales='linear', units='V')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Short FFT" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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ElR3yT/VesXBTfStDw6roAHk+fUB0guquebT8WGaiAQAAgESUaAAAACARJRoAAABIRIkG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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax1 = plt.subplots(1, 1, figsize=(12,6))\n", "P, freqs, t, im = plt.specgram(y, NFFT=64, Fs=freq, noverlap = 32, cmap=plt.cm.gist_heat)\n", "# P: array of shape (len(times), len(freqs)) of power,\n", "# freqs: array of frequencies, \n", "# bins: time points the spectrogram is calculated over,\n", "# im: matplotlib.image.AxesImage instance\n", "ax1.set_title('Short FFT', fontsize=18);\n", "ax1.set_xlabel('Time [s]'); ax1.set_ylabel('Frequency [Hz]');" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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bQoNNlJukVidMlcYkykI2p5Zke0Tg4Dr7mdPHhNzc0fv2TB/zhtDSHjdePn3M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\nA4nQzaHM9TGBt0fHpRoPTw7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.signal\n", "t = np.linspace(0, (2**12-1)/1000, 2**12)\n", "c = scipy.signal.chirp(t, f0=100, f1=300, t1=t[-1], method='linear')\n", "fig, ax1 = plt.subplots(1, 1, figsize=(12,6))\n", "P, freqs, t, im = plt.specgram(c, NFFT=256, Fs=t.size/t[-1], noverlap = 128, cmap=plt.cm.gist_heat)\n", "ax1.set_title('Short FFT', fontsize=18);\n", "ax1.set_xlabel('Time [s]'); ax1.set_ylabel('Frequency [Hz]');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Function psd.py" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# %load ./../functions/psd.py\n", "#!/usr/bin/env python\n", "\n", "\"\"\"Estimate power spectral density characteristcs using Welch's method.\"\"\"\n", "\n", "from __future__ import division, print_function\n", "import numpy as np\n", "\n", "__author__ = 'Marcos Duarte, https://github.com/demotu/BMC'\n", "__version__ = 'tnorm.py v.1 2013/09/16'\n", "\n", "\n", "def psd(x, fs=1.0, window='hanning', nperseg=None, noverlap=None, nfft=None,\n", " detrend='constant', show=True, ax=None, scales='linear', xlim=None,\n", " units='V'):\n", " \"\"\"Estimate power spectral density characteristcs using Welch's method.\n", "\n", " This function is just a wrap of the scipy.signal.welch function with\n", " estimation of some frequency characteristcs and a plot. For completeness,\n", " most of the help from scipy.signal.welch function is pasted here.\n", "\n", " Welch's method [1]_ computes an estimate of the power spectral density\n", " by dividing the data into overlapping segments, computing a modified\n", " periodogram for each segment and averaging the periodograms.\n", "\n", " Parameters\n", " ----------\n", " x : array_like\n", " Time series of measurement values\n", " fs : float, optional\n", " Sampling frequency of the `x` time series in units of Hz. Defaults\n", " to 1.0.\n", " window : str or tuple or array_like, optional\n", " Desired window to use. See `get_window` for a list of windows and\n", " required parameters. If `window` is array_like it will be used\n", " directly as the window and its length will be used for nperseg.\n", " Defaults to 'hanning'.\n", " nperseg : int, optional\n", " Length of each segment. Defaults to half of `x` length.\n", " noverlap: int, optional\n", " Number of points to overlap between segments. If None,\n", " ``noverlap = nperseg / 2``. Defaults to None.\n", " nfft : int, optional\n", " Length of the FFT used, if a zero padded FFT is desired. If None,\n", " the FFT length is `nperseg`. Defaults to None.\n", " detrend : str or function, optional\n", " Specifies how to detrend each segment. If `detrend` is a string,\n", " it is passed as the ``type`` argument to `detrend`. If it is a\n", " function, it takes a segment and returns a detrended segment.\n", " Defaults to 'constant'.\n", " show : bool, optional (default = False)\n", " True (1) plots data in a matplotlib figure.\n", " False (0) to not plot.\n", " ax : a matplotlib.axes.Axes instance (default = None)\n", " scales : str, optional\n", " Specifies the type of scale for the plot; default is 'linear' which\n", " makes a plot with linear scaling on both the x and y axis.\n", " Use 'semilogy' to plot with log scaling only on the y axis, 'semilogx'\n", " to plot with log scaling only on the x axis, and 'loglog' to plot with\n", " log scaling on both the x and y axis.\n", " xlim : float, optional\n", " Specifies the limit for the `x` axis; use as [xmin, xmax].\n", " The defaukt is `None` which sets xlim to [0, Fniquist].\n", " units : str, optional\n", " Specifies the units of `x`; default is 'V'.\n", "\n", " Returns\n", " -------\n", " Fpcntile : 1D array\n", " frequency percentiles of the power spectral density\n", " For example, Fpcntile[50] gives the median power frequency in Hz.\n", " mpf : float\n", " Mean power frequency in Hz.\n", " fmax : float\n", " Maximum power frequency in Hz.\n", " Ptotal : float\n", " Total power in `units` squared.\n", " f : 1D array\n", " Array of sample frequencies in Hz.\n", " P : 1D array\n", " Power spectral density or power spectrum of x.\n", "\n", " See Also\n", " --------\n", " scipy.signal.welch\n", "\n", " Notes\n", " -----\n", " An appropriate amount of overlap will depend on the choice of window\n", " and on your requirements. For the default 'hanning' window an\n", " overlap of 50% is a reasonable trade off between accurately estimating\n", " the signal power, while not over counting any of the data. Narrower\n", " windows may require a larger overlap.\n", " If `noverlap` is 0, this method is equivalent to Bartlett's method [2]_.\n", "\n", " References\n", " ----------\n", " .. [1] P. Welch, \"The use of the fast Fourier transform for the\n", " estimation of power spectra: A method based on time averaging\n", " over short, modified periodograms\", IEEE Trans. Audio\n", " Electroacoust. vol. 15, pp. 70-73, 1967.\n", " .. [2] M.S. Bartlett, \"Periodogram Analysis and Continuous Spectra\",\n", " Biometrika, vol. 37, pp. 1-16, 1950.\n", "\n", " Examples (also from scipy.signal.welch)\n", " --------\n", " #Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by\n", " # 0.001 V**2/Hz of white noise sampled at 10 kHz and calculate the PSD:\n", " >>> from psd import psd\n", " >>> fs = 10e3\n", " >>> N = 1e5\n", " >>> amp = 2*np.sqrt(2)\n", " >>> freq = 1234.0\n", " >>> noise_power = 0.001 * fs / 2\n", " >>> time = np.arange(N) / fs\n", " >>> x = amp*np.sin(2*np.pi*freq*time)\n", " >>> x += np.random.normal(scale=np.sqrt(noise_power), size=time.shape)\n", " >>> psd(x, fs=freq);\n", " \"\"\"\n", "\n", " from scipy import signal, integrate\n", "\n", " if not nperseg:\n", " nperseg = np.ceil(len(x) / 2)\n", " f, P = signal.welch(x, fs, window, nperseg, noverlap, nfft, detrend)\n", " Area = integrate.cumtrapz(P, f, initial=0)\n", " Ptotal = Area[-1]\n", " mpf = integrate.trapz(f * P, f) / Ptotal # mean power frequency\n", " fmax = f[np.argmax(P)]\n", " # frequency percentiles\n", " inds = [0]\n", " Area = 100 * Area / Ptotal # + 10 * np.finfo(np.float).eps\n", " for i in range(1, 101):\n", " inds.append(np.argmax(Area[inds[-1]:] >= i) + inds[-1])\n", " fpcntile = f[inds]\n", "\n", " if show:\n", " _plot(x, fs, f, P, mpf, fmax, fpcntile, scales, xlim, units, ax)\n", "\n", " return fpcntile, mpf, fmax, Ptotal, f, P\n", "\n", "\n", "def _plot(x, fs, f, P, mpf, fmax, fpcntile, scales, xlim, units, ax):\n", " \"\"\"Plot results of the ellipse function, see its help.\"\"\"\n", " try:\n", " import matplotlib.pyplot as plt\n", " except ImportError:\n", " print('matplotlib is not available.')\n", " else:\n", " if ax is None:\n", " fig, ax = plt.subplots(1, 1, figsize=(7, 5))\n", " if scales.lower() == 'semilogy' or scales.lower() == 'loglog':\n", " ax.set_yscale('log')\n", " if scales.lower() == 'semilogx' or scales.lower() == 'loglog':\n", " ax.set_xscale('log')\n", " ax.plot(f, P, linewidth=2)\n", " ylim = ax.get_ylim()\n", " ax.plot([fmax, fmax], [np.max(P), np.max(P)], 'ro',\n", " label='Fpeak = %.2f' % fmax)\n", " ax.plot([fpcntile[50], fpcntile[50]], ylim, 'r', lw=1.5,\n", " label='F50%% = %.2f' % fpcntile[50])\n", " ax.plot([mpf, mpf], ylim, 'r--', lw=1.5,\n", " label='Fmean = %.2f' % mpf)\n", " ax.plot([fpcntile[95], fpcntile[95]], ylim, 'r-.', lw=2,\n", " label='F95%% = %.2f' % fpcntile[95])\n", " leg = ax.legend(loc='best', numpoints=1, framealpha=.5,\n", " title='Frequencies [Hz]')\n", " plt.setp(leg.get_title(), fontsize=12)\n", " ax.set_xlabel('Frequency [$Hz$]', fontsize=12)\n", " ax.set_ylabel('Magnitude [%s$^2/Hz$]' % units, fontsize=12)\n", " ax.set_title('Power spectral density', fontsize=12)\n", " if xlim:\n", " ax.set_xlim(xlim)\n", " ax.set_ylim(ylim)\n", " plt.tight_layout()\n", " plt.show()\n" ] } ], "metadata": { "anaconda-cloud": {}, "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 1 }