{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic properties of signals\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": [ "A signal is a set of data that conveys information about some phenomenon (Bendat, Piersol 2010; Lathi 2009; Lyons 2010). A signal can be represented mathematically by a function of one or more independent variables. We also refer to signal as simply data. The time-dependent voltage of an electric circuit and the acceleration of a moving body are examples of signals. \n", "\n", "Let's see now a brief description about the basic properties of signals (for a more detailed description, see Bendat, Piersol 2010; Lathi 2009; Lyons 2010; Smith 1997)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Amplitude, frequency, period, and phase\n", "\n", "A periodic function can be characterized by the properties: amplitude, frequency, period, and phase. Let's exemplify these properties for a periodic function composed by a single frequency, the sine wave or sinusoid [trigonometric function](http://en.wikipedia.org/wiki/Trigonometric_functions):\n", "\n", "$$x(t) = A\\sin(2 \\pi f t + \\phi)$$\n", "\n", "Where $A$ is the amplitude, $f$ the frequency, $\\phi$ the phase, and $T=1/f$ the period of the function $x(t)$. \n", "\n", "We can define $\\omega=2\\pi f = 2\\pi/T$ as the angular frequency, then:\n", "\n", "$$x(t) = A\\sin(\\omega t + \\phi)$$\n", "\n", "Let's visualize this function:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:08:39.303536Z", "start_time": "2017-12-30T08:08:39.066942Z" } }, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import sys\n", "sys.path.insert(1, r'./../functions') # directory of BMC Python functions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:08:40.307624Z", "start_time": "2017-12-30T08:08:40.297248Z" } }, "outputs": [], "source": [ "t = np.linspace(-2, 2, 101) # time vector\n", "A = 2 # amplitude\n", "freq = 0.5 # frequency, Hz\n", "phase = np.pi/4 # phase, radians (45o)\n", "x1 = 1 * np.sin(2 * np.pi * 1 * t + 0) # sinusoid 1\n", "x2 = A * np.sin(2 * np.pi * freq * t + phase) # sinusoid 2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:08:41.829023Z", "start_time": "2017-12-30T08:08:41.184890Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from wave_plot import wave_plot\n", "ax = wave_plot(freq, t, x1, x2, ax=None)\n", "%config InlineBackend.close_figures=False # hold plot for next cell" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can you guess the shape of the sum of the two curves we just plotted?\n", "\n", "$$x_3 = x_1 + x_2$$\n", "\n", "$$x_3 = \\sin(2 \\pi t) + 2\\sin(4 \\pi t + \\pi/4)$$\n", "\n", "And here is the plot:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:08:45.432597Z", "start_time": "2017-12-30T08:08:45.143825Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x3 = x1 + x2\n", "\n", "ax.plot(t, x3, 'r', linewidth=8)\n", "ax.annotate(r'$x_3 = x_1 + x_2$', xy=(1.25, 2.2), xycoords = 'data', size=22, color='r')\n", "ax.set_ylim((-2.1, 3.1))\n", "%config InlineBackend.close_figures=True # hold off the figure\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Magnitude and power\n", "\n", "Other terms related to amplitude are magnitude and power. The magnitude is the absolute value (without the signal) of the amplitude. The power of a signal is proportional to its amplitude (or magnitude) squared." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Periodic function, fundamental frequency, and harmonics\n", "\n", "A function is said to be periodic with period $T$ if $x(t+T) = x(t)$ for all values of $t$, that is, the function repeats itself after a period. Important properties of this definition are that the sum of periodic functions and a constant times a periodic function are also periodic functions. In particular, this means that a periodic function also repeats itself after $2T,\\: 3T, \\dots$. \n", "The shortest period that the function repeats itself (in this case, $T$) is said to be the fundamental period and its inverse, the fundamental frequency of the periodic function. A [harmonic](http://en.wikipedia.org/wiki/Harmonic) is a component frequency of the function that is an integer multiple of the fundamental frequency, i.e., the harmonics have frequencies $f,\\: 2f,\\: 3f, \\dots$ (which have periods $T,\\: T/2,\\: T/3, \\dots$) and are referred as the first, second, and third harmonics, respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## AC and DC components\n", "\n", "A periodic function can also be characterized by its [AC and DC components](http://en.wikipedia.org/wiki/DC_bias). These terms originated in electronics and mean alternate current and direct current, respectively. The DC component, also referred as DC offset or DC bias, is simply the average (mean) value of the function, i.e., the constant part of the function. The AC component is the oscillatory part of the function and can be found by subtracting the function average value (the DC component) from the function itself. \n", "The next figure illustrates these components." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:09:04.974335Z", "start_time": "2017-12-30T08:09:04.663679Z" }, "run_control": { "breakpoint": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ac_dc_plot import ac_dc_plot\n", "ax = ac_dc_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that for a periodic function like $x(t)=A\\cos(2\\pi f t)$, when its frequency is zero, $x(t)=A$. That is, the function $x(t)$ has only a DC component (if $A$ is different from zero). Because that, we can say that the DC component of a function has a frequency equals to zero (an infinite period)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Even and odd functions\n", "\n", "[Even and odd functions](http://en.wikipedia.org/wiki/Even_and_odd_functions) are functions which satisfy symmetry relations with respect to taking additive inverses. The [additive inverse](http://en.wikipedia.org/wiki/Additive_inverse) of a number x is the number that added to x yields zero. \n", "\n", "The function $x(t)$ is even if $x(t) = x(-t)$ and $x(t)$ is odd if $x(t) = -x(-t)$.\n", "\n", "The cosine function is even, for instance, $\\cos(\\pi)=\\cos(-\\pi)$, and the sine function is odd, for instance, $\\sin(\\pi/2)=-\\sin(-\\pi/2)$; confer the next figure. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:09:11.583070Z", "start_time": "2017-12-30T08:09:11.231596Z" }, "run_control": { "breakpoint": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from even_odd_plot import even_odd_plot\n", "ax = even_odd_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Continuous and discrete signals\n", "\n", "A [continuous signal](http://en.wikipedia.org/wiki/Continuous_signal) is dependent of a continuous variable, that is, the independent variable varies continuously (it has a continuum domain). On the other hand, a [discrete signal](http://en.wikipedia.org/wiki/Discrete-time_signal) is dependent of a discrete variable, that is, the independent variable is defined only on a discrete set of values. For instance, the temperature throughout the day (T(t)) is a continuous signal in the sense it depends on time, which varies continuously. However, if we measure the temperature only at certain times, let's say every hour, then this new signal is discrete because its independent variable is discrete (t= 8 am, 9 am, 10 am, ...). \n", "The following figure illustrates continuous and discrete signals (however, since we are using a digital computer, the continuous signal below is in fact not authentic!):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:09:20.368733Z", "start_time": "2017-12-30T08:09:20.080385Z" }, "run_control": { "breakpoint": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from cont_disc_plot import cont_disc_plot\n", "ax = cont_disc_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sampling\n", "\n", "The reduction of a continuous signal to a discrete signal is called sampling and the frequency which this is performed is called sampling frequency or sampling rate. The unit of the sampling frequency is hertz (Hz). For instance, the discrete signal plotted above has a sampling frequency of 20 Hz (the data were sampled at a 0.05 s interval).\n", "\n", "Sampling is the basis for using digital computers to record and store data from a observed phenomenon. As computers have a finite memory, one can not store a continuous signal (how many instants are in a period of one second?). This leads us to the related property: analog and digital signals." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Nyquist-Shannon sampling theorem\n", "\n", "Some requirements must be satisfied for the proper discretization of a signal and an important one is expressed in the [Nyquist-Shannon sampling theorem](http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem), which is given by (Shannon's version): \n", "> *\"If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.\"* \n", "\n", "That is, to appropriately acquire data from some phenomenon which its highest frequency component is $f_B$, the sampling frequency ($fs$) must be at least two times that, $fs\\geq2f_B$. The Nyquist frequency (the highest possible frequency in the acquired (sampled) signal) is half of the sampling frequency.\n", "\n", "When the Nyquist-Shannon sampling theorem is not satisfied and a continuous signal is discretized with a frequency less than two times of its highest frequency, it occurs an effect called [aliasing](http://en.wikipedia.org/wiki/Aliasing). In this case, the discrete signal does not contain the same information as the continuous signal. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analog and digital signals\n", "\n", "The amplitude of an [analog signal](http://en.wikipedia.org/wiki/Analog_signal) can take on any value (an infinite number of possible values) in a continuous range. On the other hand, the amplitude of a [digital signal](http://en.wikipedia.org/wiki/Digital_signal) can take only certain values (a finite number of possible values). For instance, a binary signal can take only two values.\n", "\n", "The continuous and discrete properties refer to the independent variable (for instance, time) and the analog and digital properties refer to the amplitude of the dependent variable (the signal itself)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quantization\n", "\n", "The reduction of an analog signal to a digital signal is called quantization and in the context of measurement this is typically performed by an [analog-to-digital (A/D) converter](http://en.wikipedia.org/wiki/Analog-to-digital_converter). The number of discrete values of the signal amplitude over the range of the measured signal is the resolution of the quantization. Because digital computers are often employed in this process, resolution is expressed in number of bits and is a power of two. For instance, a resolution of 1 bit can encode an analog input to one in 2 ($2^0$) different levels, a resolution of 4 bits can encode an analog input to one in 16 ($2^4$) different levels, and a good commercial A/D converter has a resolution of 16 bits ($2^16$=65536 levels).\n", "\n", "If we know the voltage range (maximum minus minimum signal that can be read) of a A/D converter, we can express the resolution in Volts. For instance, a typical range is 10 V [-5V, 5V]; for 1 bit the resolution is 5 V, for 4 bits is 0.625, and for 16 bits is around 0.00015 V (0.15 mV), as illustrated in the next figure." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2017-12-30T08:09:40.368968Z", "start_time": "2017-12-30T08:09:39.960388Z" }, "run_control": { "breakpoint": false } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from quantize_plot import quantize_plot\n", "ax = quantize_plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deterministic and random signals\n", "\n", "A deterministic signal can be described by an explicit mathematical function. On other hand, a random signal cannot be described by an explicit mathematical function. A sine wave and a parabola are examples of deterministic signals. The outcomes of throwing a coin and a dice are random. Although the set of possible values are limited and known, there is no mathematical function to predict the exact outcome; just its probability of happening. Most measurements of observed phenomena in nature contain both deterministic and random signals. \n", "\n", "Since by definition there is no explicit mathematical function to generate a random signal, computers in fact are unable to generate true random data. For that, one needs to extract data from nature and inject into the computer! Read more about that in [Introduction to Randomness and Random Numbers](http://www.random.org/randomness/). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Signal and noise\n", "\n", "With respect to what is being measured, data can be classified as signal or noise. \n", "Signal is what you want of the phenomenon and you believe this signal truly represents the phenomenon being measured (or modeled) and [noise](http://en.wikipedia.org/wiki/Noise) is what you don't want in a measurement because, in principle, it has no significant role to the understanding of the observed phenomenon. \n", "As much as this argument is tautological, the distinction between noise and signal depends on what you think is relevant about the observed phenomenon. Experimental data are contaminated by noise and it is rarely possible to completely distinguish signal from noise. \n", "[Signal-to-Noise ratio](http://en.wikipedia.org/wiki/Signal-to-noise_ratio) (SNR or S/N) is a measure to quantify the level of a desired signal in relation to the level of background noise. It is defined as the ratio between the power of the signal content and the power of the noise content in some data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Signal and system\n", "\n", "In engineering, signal is often associated to a system, which is an entity (a physical or virtual device) that takes a signal as input and produces another signal as output. In mathematics, if a signal can be represented as a function, the analogous for a system is to be represented as a differential equation. For instance, a mass attached to a spring is a system which can take a force (signal) as input and produce a displacement (another signal). This system could be described by a second-order ordinary differential equation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problems\n", "\n", "1. Plot the following functions in the interval $t=[-1, 1]$: \n", " a) $x(t) = 1 + 0.5\\cos(t + \\pi/4)$ \n", " b) $x(t) = |t|$ \n", " c) $x(t) = 2x^3$ \n", " d) $x(t) = \\sin(2\\pi t) + \\cos(2\\pi t)$ \n", " e) $x(t) = \\sin^2(2\\pi t) + \\cos^2(2\\pi t)$ \n", " f) $x(t) = \\sin(2\\pi t)/t$ \n", "\n", "2. Plot the following function in the interval $t=[-3\\pi, 3\\pi]$: \n", "$$x(t) = \\left\\{ \n", "\\begin{array}{l l}\n", " 1+t/\\pi & \\quad \\text{if } -\\pi < t < 0\\\\\n", " 1-t/\\pi & \\quad \\text{if } 0 < t < +\\pi\n", "\\end{array} \\right.$$\n", "$$x(t + 2\\pi) = x(t), \\quad \\text{for all } t$$ \n", "\n", "3. Which are the amplitude, frequency, period, and phase of the functions in problems 1 and 2? \n", "\n", "4. Calculate the AC and DC components for the functions in problems 1 and 2. \n", "\n", "5. Which functions are even or odd in problems 1 and 2? \n", " \n", "6. The [power line frequency](http://en.wikipedia.org/wiki/Utility_frequency) in Brazil is about 60 Hz (same frequency in US and in Europe is 50 Hz, [see an on line measurement of the frequency in Europe here](http://www.mainsfrequency.com/)). The amplitude of the power line is usually 110 V RMS, where RMS stands for root mean square. \n", "For a discrete signal, RMS is given by:\n", "$$RMS = \\sqrt{\\frac{1}{N}\\sum_{i=1}^{N} x_i^2}$$\n", "And for a continuous periodic signal with period $T$, RMS is given by:\n", "$$RMS = \\frac{1}{T}\\int_{t_0}^{t_0+T} (x(t))^2 \\:\\mathrm{d}t$$\n", "If the power line waveform is a sinusoid, which is its amplitude that results in 110 V RMS? \n", "\n", "7. Calculate the average power and the RMS values for the signals in problem 1. \n", "\n", "8. Consider the continuous signal represented by the function $x(t) = 2\\sin(8\\pi t)$. \n", " a) Which would be the Nyquist frequency ($f_N$) of this signal? \n", " b) Plot discretized versions of this signal for the following sampling frequencies: $10f_N$, $2f_N$, $f_N$, and $f_N/2$. \n", " \n", "9. In scientific computing, it's common to use a random number generator to generate noise and add that to a signal.\n", "For example, the following code generates a sinusoid (signal) plus a random noise: \n", "python \n", "t = np.linspace(0, 1, .01)\n", "x = np.sin(2*2*np.pi*t) + np.random.randn(t.size)/10\n", " \n", "Plot this function and play with different levels of noise. \n", "\n", "10. Write a code in Python that for a given input signal, calculates its average value, peak-to-peak amplitude, average power, and RMS values." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "- Bendat JS, Piersol AG (2010) [Random Data: Analysis and Measurement Procedures](http://books.google.com.br/books?id=qYSViFRNMlwC). 4th Edition. John Wiley & Sons, Inc.\n", "- [dspGuru - Digital Signal Processing Central](http://www.dspguru.com/).\n", "- Lathi BP (2009) [Linear Systems and Signals](http://books.google.com.br/books?id=JC18PwAACAAJ). Oxford University Press.\n", "- Lyons RG (2010) [Understanding Digital Signal Processing](http://books.google.com.br/books?id=UBU7Y2tpwWUC&hl). 3rd edition. Prentice Hall.\n", "- Smith SW (1997) [The Scientist and Engineer's Guide to Digital Signal Processing](http://www.dspguide.com/). California Technical Pub." ] } ], "metadata": { "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": "3.6.4" }, "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 }