{ "cells": [ { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "# Spectral Analysis of Deterministic Signals\n", "\n", "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "Signals emerging from electrical/mechanical oscillatory systems have a specific structure. They are composed of a superposition of harmonic signals with different frequencies and amplitudes. Many practical signals are composed of (superpositions of) harmonic signals. [Estimating the number of harmonic signals, their frequencies, amplitudes, and phases](https://en.wikipedia.org/wiki/Modal_analysis) is an essential task in the analysis of unknown signals. In the practical realization of spectral analysis techniques, the [discrete Fourier transform](https://en.wikipedia.org/wiki/Discrete_Fourier_transform) (DFT) is applied to discrete finite-length signals to gain insights into their spectral composition. For instance, using a [Spectrum analyzer](https://en.wikipedia.org/wiki/Spectrum_analyzer). However, analyzing harmonic signals with the DFT is subject to fundamental limitations. These limitations are discussed in the following." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Leakage Effect\n", "\n", "[Spectral leakage](https://en.wikipedia.org/wiki/Spectral_leakage) is a fundamental effect of the DFT. It limits the ability to detect harmonic signals in signal mixtures and hence the performance of spectral analysis. In order to discuss this effect, the DFT of a discrete exponential signal is revisited starting from the Fourier transform of the continuous exponential signal. The connections between the Fourier transform, the [discrete-time Fourier transform](https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform) (DTFT) and the DFT for a uniformly sampled signal are illustrated below.\n", "\n", "![Connections between the different Fourier transforms](Fourier_transforms.png)\n", "\n", "Consequently, the leakage effect is discussed in the remainder of this section by considering the following four steps:\n", "\n", "1. Fourier transform of an harmonic exponential signal,\n", "2. discrete-time Fourier transform (DTFT) of a discrete harmonic exponential signal, and\n", "3. DTFT of a finite-length discrete harmonic exponential signal\n", "4. sampling of the DTFT." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fourier Transform of an Exponential Signal\n", "\n", "The harmonic exponential signal is defined as\n", "\n", "\\begin{equation}\n", "x(t) = \\mathrm{e}^{\\,\\mathrm{j}\\, \\omega_0 \\, t}\n", "\\end{equation}\n", "\n", "where $\\omega_0 = 2 \\pi f$ denotes the angular frequency of the signal. The Fourier transform of the exponential signal is\n", "\n", "\\begin{equation}\n", "X(\\mathrm{j}\\, \\omega) = \\int\\limits_{-\\infty}^{\\infty} x(t) \\,\\mathrm{e}^{\\,- \\mathrm{j}\\, \\omega \\,t} \\mathrm{d}t = 2\\pi \\; \\delta(\\omega - \\omega_0)\n", "\\end{equation}\n", "\n", "The spectrum consists of a single shifted Dirac impulse located at the angular frequency $\\omega_0$ of the exponential signal. Hence the spectrum $X(\\mathrm{j}\\, \\omega)$ consists of a clearly isolated and distinguishable event. In practice, it is not possible to compute the Fourier transform of a continuous signal by means of digital signal processing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discrete-Time Fourier Transform of a Discrete Exponential Signal\n", "\n", "Now lets consider sampled signals. The discrete exponential signal $x[k]$ is derived from its continuous counterpart $x(t)$ above by equidistant sampling $x[k] := x(k T)$ with the sampling interval $T$\n", "\n", "\\begin{equation}\n", "x[k] = \\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega_0 \\,k}\n", "\\end{equation}\n", "\n", "where $\\Omega_0 = \\omega_0 T$ denotes the normalized angular frequency. The DTFT is the Fourier transform of a sampled signal. For the exponential signal it is given as (see e.g. [reference card discrete signals and systems](../reference_cards/RC_discrete_signals_and_systems.pdf))\n", "\n", "\\begin{equation}\n", "X(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega}) = \\sum_{k = -\\infty}^{\\infty} x[k]\\, \\mathrm{e}^{\\,-\\mathrm{j}\\, \\Omega \\,k} = 2\\pi \\sum_{n = -\\infty}^{\\infty} \\delta((\\Omega-\\Omega_0) - 2\\,\\pi\\,n)\n", "\\end{equation}\n", "\n", "The spectrum of the DTFT is $2\\pi$-periodic due to sampling. As a consequence, the transform of the discrete exponential signal consists of a series Dirac impulses. For the region of interest $-\\pi < \\Omega \\leq \\pi$ the spectrum consists of a clearly isolated and distinguishable event, as for the continuous case.\n", "\n", "The DTFT cannot be realized in practice, since is requires the knowledge of the signal $x[k]$ for all time instants $k$. In general, a measured signal is only known within a finite time-interval. The DFT of a signal of finite length can be derived from the DTFT in two steps:\n", "\n", "1. truncation (windowing) of the signal and\n", "2. sampling of the DTFT spectrum of the windowed signal.\n", "\n", "The consequences of these two steps are investigated in the following." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discrete-Time Fourier Transform of a Truncated Discrete Exponential Signal\n", "\n", "In general, truncation of a signal $x[k]$ to a length of $N$ samples is modeled by multiplying the signal with a window function $w[k]$ of length $N$\n", "\n", "\\begin{equation}\n", "x_N[k] = x[k] \\cdot w[k]\n", "\\end{equation}\n", "\n", "where $x_N[k]$ denotes the truncated signal and $w[k] = 0$ for $\\{k: k < 0 \\vee k \\geq N \\}$. The spectrum $X_N(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})$ can be derived from the multiplication theorem of the DTFT as\n", "\n", "\\begin{equation}\n", "X_N(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega}) = \\frac{1}{2 \\pi} X(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega}) \\circledast_{2 \\pi} W(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})\n", "\\end{equation}\n", "\n", "where $\\circledast_{2 \\pi}$ denotes a cyclic/[circular convolution](https://en.wikipedia.org/wiki/Circular_convolution) of period $2 \\pi$. A hard truncation of the signal to $N$ samples is modeled by the rectangular signal \n", "\n", "\\begin{equation}\n", "w[k] = \\text{rect}_N[k] = \\begin{cases}\n", "1 & \\mathrm{for} \\; 0\\leq k" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "Om0 = 1 # frequency of exponential signal\n", "N = 32 # length of signal\n", "\n", "\n", "# DTFT of finite length exponential signal (analytic)\n", "Om = np.linspace(-np.pi, np.pi, num=1024)\n", "XN = (\n", " np.exp(-1j * (Om - Om0) * (N - 1) / 2)\n", " * (np.sin(N * (Om - Om0) / 2))\n", " / (np.sin((Om - Om0) / 2))\n", ")\n", "\n", "# plot spectrum\n", "plt.figure(figsize=(10, 8))\n", "plt.plot(Om, abs(XN))\n", "plt.title(\n", " r\"Absolute value of the DTFT of a truncated exponential signal \"\n", " + r\"$e^{{j \\Omega_0 k}}$ with $\\Omega_0=${0:1.2f}\".format(Om0)\n", ")\n", "plt.xlabel(r\"$\\Omega$\")\n", "plt.ylabel(r\"$|X_N(e^{j \\Omega})|$\")\n", "plt.axis([-np.pi, np.pi, -0.5, N + 5])\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Change the frequency `Om0` of the signal and rerun the example. How does the magnitude spectrum change?\n", "* Change the length `N` of the signal and rerun the example. How does the magnitude spectrum change?\n", "\n", "Solution: The maximum of the absolute value of the spectrum is located at the frequency $\\Omega_0$. It should become clear that truncation of the exponential signal leads to a broadening of the spectrum. The shorter the signal, the wider the mainlobe becomes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Leakage Effect of the Discrete Fourier Transform\n", "\n", "The DFT is derived from the DTFT $X_N(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})$ of the truncated signal $x_N[k]$ by sampling the DTFT equidistantly at $\\Omega = \\mu \\frac{2 \\pi}{N}$\n", "\n", "\\begin{equation}\n", "X[\\mu] = X_N(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})\\big\\vert_{\\Omega = \\mu \\frac{2 \\pi}{N}}\n", "\\end{equation}\n", "\n", "For the DFT of the exponential signal we finally get\n", "\n", "\\begin{equation}\n", "X[\\mu] = \\mathrm{e}^{\\,- \\mathrm{j}\\, (\\mu \\frac{2 \\pi}{N} - \\Omega_0) \\frac{N-1}{2}} \\cdot \\frac{\\sin(\\frac{N \\,(\\mu \\frac{2 \\pi}{N} - \\Omega_0)}{2})}{\\sin(\\frac{\\mu \\frac{2 \\pi}{N} - \\Omega_0)}{2})}\n", "\\end{equation}\n", "\n", "The sampling of the DTFT is illustrated in the following example. Note that the normalized angular frequency $\\Omega_0$ has been expressed in terms of the periodicity $P$ of the exponential signal $\\Omega_0 = P \\; \\frac{2\\pi}{N}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 32 # length of the signal\n", "P = 10.33 # periodicity of the exponential signal\n", "Om0 = P * (2 * np.pi / N) # frequency of exponential signal\n", "\n", "\n", "# truncated exponential signal\n", "k = np.arange(N)\n", "x = np.exp(1j * Om0 * k)\n", "\n", "# DTFT of finite length exponential signal (analytic)\n", "Om = np.linspace(0, 2 * np.pi, num=1024)\n", "Xw = (\n", " np.exp(-1j * (Om - Om0) * (N - 1) / 2)\n", " * (np.sin(N * (Om - Om0) / 2))\n", " / (np.sin((Om - Om0) / 2))\n", ")\n", "\n", "# DFT of the exponential signal by FFT\n", "X = np.fft.fft(x)\n", "mu = np.arange(N) * 2 * np.pi / N\n", "\n", "# plot spectra\n", "plt.figure(figsize=(10, 8))\n", "ax1 = plt.gca()\n", "\n", "plt.plot(Om, abs(Xw), label=r\"$|X_N(e^{j \\Omega})|$\")\n", "plt.stem(mu, abs(X), label=r\"$|X_N[\\mu]|$\", basefmt=\" \", linefmt=\"C1\", markerfmt=\"C1o\")\n", "plt.ylim([-0.5, N + 5])\n", "plt.title(\n", " r\"Absolute value of the DTFT/DFT of a truncated exponential signal \"\n", " + r\"$e^{{j \\Omega_0 k}}$ with $\\Omega_0=${0:1.2f}\".format(Om0),\n", " y=1.08,\n", ")\n", "plt.legend()\n", "\n", "ax1.set_xlabel(r\"$\\Omega$\")\n", "ax1.set_xlim([Om[0], Om[-1]])\n", "ax1.grid()\n", "\n", "ax2 = ax1.twiny()\n", "ax2.set_xlim([0, N])\n", "ax2.set_xlabel(r\"$\\mu$\", color=\"C1\")\n", "ax2.tick_params(\"x\", colors=\"C1\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise**\n", "\n", "* Change the periodicity `P` of the exponential signal and rerun the example. What happens if the periodicity is an integer? Why?\n", "* Change the length `N` of the DFT? How does the spectrum change?\n", "* What conclusions can be drawn for the analysis of a single exponential signal by the DFT?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solution: You should have noticed that for an exponential signal whose periodicity is an integer $P \\in \\mathbb{N}$, the DFT consists of a discrete Dirac pulse $X[\\mu] = N \\cdot \\delta[\\mu - P]$. In this case, the sampling points coincide with the maximum of the main lobe or the zeros of the DTFT. For non-integer $P$, hence non-periodic exponential signals with respect to the signal length $N$, the DFT has additional contributions. The shorter the length $N$, the wider these contributions are spread in the spectrum. This smearing effect is known as *leakage effect* of the DFT. It can be concluded from inspection of the maximumum value of above DFT, that estimating the unknown frequency and amplitude of an exponential signal from its DFT may lead to inaccuracies." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Analysis of Signal Mixtures by the Discrete Fourier Transform\n", "\n", "The limitations imposed by the leakage effect have also implications for the analysis of signal mixtures. In order to discuss these implications when analyzing signal mixtures, the superposition of two exponential signals with different amplitudes and frequencies is considered\n", "\n", "\\begin{equation}\n", "x_N[k] = A_1 \\cdot e^{\\mathrm{j} \\Omega_1 k} + A_2 \\cdot e^{\\mathrm{j} \\Omega_2 k}\n", "\\end{equation}\n", "\n", "where $A_1, A_2 \\in \\mathbb{R}$. The effects are discussed using numerical simulations. For convenience, a function is defined that calculates and plots the magnitude spectrum of $x_N[k]$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def dft_signal_mixture(N, *, amp1, period1, amp2, period2):\n", " \"\"\"Calculates and plots the magnitude spectrum of two superimposed exponentials.\n", "\n", " Keyword arguments:\n", " N: length of signal/DFT\n", " amp1, period1 : amplitude and periodicity of 1st complex exponential\n", " amp2, period2 : amplitude and periodicity of 2nd complex exponential\n", " \"\"\"\n", "\n", " # generate the signal mixture\n", " Om0_1 = period1 * (2 * np.pi / N) # frequency of 1st exponential signal\n", " Om0_2 = period2 * (2 * np.pi / N) # frequency of 2nd exponential signal\n", " k = np.arange(N)\n", " x = amp1 * np.exp(1j * Om0_1 * k) + amp2 * np.exp(1j * Om0_2 * k)\n", "\n", " # DFT of the signal mixture\n", " mu = np.arange(N)\n", " X = np.fft.fft(x)\n", "\n", " # plot spectrum\n", " plt.figure(figsize=(10, 8))\n", " plt.stem(mu, abs(X), basefmt=\" \")\n", " plt.title(r\"Absolute value of the DFT of a signal mixture\")\n", " plt.xlabel(r\"$\\mu$\")\n", " plt.ylabel(r\"$|X[\\mu]|$\")\n", " plt.axis([0, N, -0.5, N + 5])\n", " plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets first consider the case that the frequencies of the two exponentials are rather far apart in terms of normalized angular frequency" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dft_signal_mixture(32, amp1=1, period1=10.3, amp2=1, period2=15.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Investigating the magnitude spectrum one could conclude that the signal consists of two major contributions at the frequencies $\\mu_1 = 10$ and $\\mu_2 = 15$. Now lets take a look at a situation where the frequencies are closer together" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dft_signal_mixture(32, amp1=1, period1=10.3, amp2=1, period2=10.9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From visual inspection of the spectrum it is rather unclear if the mixture consists of one or two exponential signals. So far the levels of both signals where chosen equal. \n", "\n", "Lets consider the case where the second signal has a much lower level that the first one. The frequencies have been chosen equal to the first example" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dft_signal_mixture(32, amp1=1, period1=10.3, amp2=0.1, period2=15.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the contribution of the second exponential is almost hidden in the spread spectrum of the first exponential. From these examples it should have become clear that the leakage effect limits the spectral resolution of the DFT." ] }, { "cell_type": "markdown", "metadata": { "nbsphinx": "hidden" }, "source": [ "**Copyright**\n", "\n", "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.6" } }, "nbformat": 4, "nbformat_minor": 4 }