python
{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Import all the needed packages" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import signal" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The basic frequency is 4.0 Hz.\n", "The harmonic frequencies are: [ 4. 8. 12.]\n" ] } ], "source": [ "SAVE_FIG = 1 # Flag to control the saving of figures: 1 -> save, 0 -> otherwise.\n", "pi = np.pi\n", "myID = 1234 # The last 4 digits of my ERAU ID\n", "np.random.seed(seed=myID) # myID is used to set the seed of the random number generator\n", "Freq_1 = np.floor((10 + np.random.randint(0,10)) / 3) # (random) frequency of signal in Hz\n", "print(\"The basic frequency is\", Freq_1, \"Hz.\")\n", "\n", "Nd = 1024 # Total number of samples for dense sampling; d stands for dense sampling\n", "Ns = Nd / 16 # Total number of samples for sparse sampling; s stands for sparse sampling\n", "Ns2 = int(Ns // 2) # Ns/2, to be used as the index for array\n", "Fs_d = Nd # Sample rate for dense sampling\n", "Fs_s = Ns # Sample rate for sparse sampling\n", "t_d = np.arange(Nd) / Fs_d # Sample times for dense sampling\n", "t_s = np.arange(Ns) / Fs_s # Sample times for sparse sampling\n", "Freq_s = np.arange(-Fs_s/2, Fs_s/2) # Frequencies for spectrum display\n", "\n", "Am = np.array([1, 0.5, 0.2]) # Amplitudes of three signals\n", "Fm = np.array([Freq_1, 2*Freq_1, 3*Freq_1]) # Frequencies of three signals\n", "Pm = np.array([np.pi/4, np.pi/3, np.pi/9]) # Phases of three signals\n", "print(\"The harmonic frequencies are: \", Fm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Task 1 Demonstrating the relationship between the waveform and spectrum of single frequency sinusoidal signals" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1affbff2a90>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 1A and 1B. Waveform and spectrum of a sinusoid signal with Am[0], Fm[0], and Pm[0]. \n", "\n", "x1_s = Am[0] * np.cos(2*np.pi*Fm[0]*t_s + Pm[0])\n", "x1_d = Am[0] * np.cos(2*np.pi*Fm[0]*t_d + Pm[0])\n", "X1_s = np.fft.fft(x1_s)\n", "X1_F = np.abs(np.fft.fftshift(X1_s))\n", "Freqint1 = int(np.round(Fm[0]*Ns/Fs_s))\n", "\n", "fig1 = plt.figure(1)\n", "plt.subplot(211) \n", "plt.plot(t_s, x1_s, 'o', t_d, x1_d)\n", "plt.axis([0, t_d[-1], -1.5, +1.5])\n", "plt.xlabel('Time')\n", "plt.ylabel('Waveform')\n", "\n", "plt.subplot(212)\n", "plt.stem(Freq_s, X1_F)\n", "plt.text(Fm[0]-2, np.abs(X1_s[Freqint1])+3, str(X1_s[Freqint1]))\n", "plt.axis([Freq_s[0], Freq_s[-1], 0, 45])\n", "plt.xlabel('Freq') \n", "plt.ylabel('Spectrum')\n", "\n", "fig = plt.gcf()\n", "fig.set_size_inches(10, 10)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1affbffc080>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 1C. Repeat 1A and 1B for a sinusoid signal with Am[1], Fm[1], and Pm[1].\n", "\n", "x2_s = Am[1] * np.cos(2*np.pi*Fm[1]*t_s + Pm[1])\n", "x2_d = Am[1] * np.cos(2*np.pi*Fm[1]*t_d + Pm[1])\n", "X2_s = np.fft.fft(x2_s)\n", "X2_F = np.abs(np.fft.fftshift(X2_s))\n", "Freqint2 = int(np.round(Fm[1]*Ns/Fs_s))\n", "\n", "fig2 = plt.figure(2)\n", "plt.subplot(211) \n", "plt.plot(t_s, x2_s, 'o', t_d, x2_d)\n", "plt.axis([0, t_d[-1], -1.5, +1.5])\n", "plt.xlabel('Time')\n", "plt.ylabel('Waveform')\n", "\n", "plt.subplot(212)\n", "plt.stem(Freq_s, X2_F)\n", "plt.text(Fm[1]-2, np.abs(X2_s[Freqint2])+3, str(X2_s[Freqint2]))\n", "plt.axis([Freq_s[0], Freq_s[-1], 0, 45])\n", "plt.xlabel('Freq') \n", "plt.ylabel('Spectrum')\n", "\n", "fig = plt.gcf()\n", "fig.set_size_inches(10, 10)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Task 2. Demonstrating the waveform and spectrum of the superposition of multiple sinusoidal signals" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[4 8]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1aff86a8080>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 2A.\n", "xx1_s = x1_s + x2_s\n", "xx1_d = x1_d + x2_d\n", "XX1_s = np.fft.fft(xx1_s)\n", "XX1_F = np.abs(np.fft.fftshift(XX1_s))\n", "peakinds, _ = signal.find_peaks(np.abs(XX1_s[0:Ns2]), height=1)\n", "print(peakinds)\n", "\n", "fig3 = plt.figure(3)\n", "plt.subplot(211) \n", "plt.plot(t_s, xx1_s, 'o', t_d, xx1_d)\n", "plt.axis([0, t_d[-1], -1.5, +1.5])\n", "plt.xlabel('Time')\n", "plt.ylabel('Waveform')\n", "\n", "plt.subplot(212)\n", "plt.stem(Freq_s, XX1_F)\n", "# One way of doing a for loop: two variables in a loop\n", "for i, peak in zip(range(len(peakinds)), peakinds):\n", " plt.text(Fm[i]-2, np.abs(XX1_s[peak])+3, str(XX1_s[peak]))\n", "plt.axis([Freq_s[0], Freq_s[-1], 0, 45])\n", "plt.xlabel('Freq') \n", "plt.ylabel('Spectrum')\n", "\n", "fig = plt.gcf()\n", "fig.set_size_inches(10, 10)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(64,) (1024,)\n", "[ 4 8 12]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x1affa9b1080>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 2B.\n", "# Generate the sparse sequence using the iteration method\n", "xx2_s = np.zeros_like(t_s)\n", "for i in range(len(Am)):\n", " xx2_s += Am[i] * np.cos(2*np.pi*Fm[i]*t_s + Pm[i]) \n", "# Generate the dense sequence using the SUM methon\n", "xx2_d = np.sum(Am.reshape(1,-1) * \n", " np.cos(2*np.pi*np.dot(t_d.reshape(-1,1),Fm.reshape(1,-1)) + Pm.reshape(1,-1)), axis=1)\n", "print(xx2_s.shape, xx2_d.shape)\n", "\n", "XX2_s = np.fft.fft(xx2_s)\n", "XX2_F = np.abs(np.fft.fftshift(XX2_s))\n", "peakinds, _ = signal.find_peaks(np.abs(XX2_s[0:Ns2]), height=1)\n", "print(peakinds)\n", "\n", "fig4 = plt.figure(4)\n", "plt.subplot(211) \n", "plt.plot(t_s, xx2_s, 'o', t_d, xx2_d)\n", "plt.axis([0, t_d[-1], -1.5, +1.5])\n", "plt.xlabel('Time')\n", "plt.ylabel('Waveform')\n", "\n", "plt.subplot(212)\n", "plt.stem(Freq_s, XX2_F)\n", "# Another way of doing a for loop: one variable in a loop\n", "for i in range(len(peakinds)):\n", " plt.text(Fm[i]-2, np.abs(XX2_s[peakinds[i]])+3, str(XX2_s[peakinds[i]]))\n", "plt.axis([Freq_s[0], Freq_s[-1], 0, 45])\n", "plt.xlabel('Freq') \n", "plt.ylabel('Spectrum')\n", "\n", "fig = plt.gcf()\n", "fig.set_size_inches(10, 10)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Figures Saved.\n" ] } ], "source": [ "if SAVE_FIG == 1:\n", " fig1.savefig('../figs/cec411_lab01_fig1.svg')\n", " fig2.savefig('../figs/cec411_lab01_fig2.svg')\n", " fig3.savefig('../figs/cec411_lab01_fig3.svg')\n", " fig4.savefig('../figs/cec411_lab01_fig4.svg')\n", " print('Figures Saved.')" ] } ], "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" } }, "nbformat": 4, "nbformat_minor": 2 }