{"nbformat_minor": 0, "cells": [{"source": "EE120 Fall 2016 PS 8, Quadrature amplitude modulation for 4 channels", "cell_type": "markdown", "metadata": {}}, {"source": "To ouput python notebook to printable format, use ``ipython nbconvert file.ipynb'' from command prompt. You may need to install pandoc first.", "cell_type": "markdown", "metadata": {}}, {"execution_count": 12, "cell_type": "code", "source": "print 4+5  # check to see if iPython is running...", "outputs": [{"output_type": "stream", "name": "stdout", "text": "9\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 13, "cell_type": "code", "source": "%pylab", "outputs": [{"output_type": "stream", "name": "stdout", "text": "Using matplotlib backend: Qt4Agg\nPopulating the interactive namespace from numpy and matplotlib\n"}, {"output_type": "stream", "name": "stderr", "text": "WARNING: pylab import has clobbered these variables: ['rate']\n`%matplotlib` prevents importing * from pylab and numpy\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 14, "cell_type": "code", "source": "import numpy as np\nimport scipy as sp\nprint 'imported numpy and scipy'\nimport matplotlib.pyplot as plt\n%matplotlib inline\nfrom scipy.io import wavfile\nprint 'numpy version is', np.__version__\nprint 'finished importing'", "outputs": [{"output_type": "stream", "name": "stdout", "text": "imported numpy and scipy\nnumpy version is 1.9.2\nfinished importing\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 15, "cell_type": "code", "source": "# Graphing helper function\ndef setup_graph(title='', x_label='', y_label='', fig_size=None):\n    fig = plt.figure()\n    if fig_size != None:\n        fig.set_size_inches(fig_size[0], fig_size[1])\n    ax = fig.add_subplot(111)\n    ax.set_title(title)\n    ax.set_xlabel(x_label)\n    ax.set_ylabel(y_label)", "outputs": [], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 16, "cell_type": "code", "source": "# Write signal to .wav files after down sampling by 16 and scaling\ndef wavwrite(name,sig,length):\n    rate1 = 44100 # CD audio quality,\n    out = np.zeros(length/16)\n    out=sig.real[0:length:16] # downsample\n    scale = 32767.0/(max(np.max(out),-np.min(out)))\n    out = np.multiply(scale,out)\n    wavfile.write(name, rate1, out.astype(np.int16)) # 16 bit integer\n    print 'wrote file',name", "outputs": [], "metadata": {"collapsed": true, "trusted": true}}, {"execution_count": 17, "cell_type": "code", "source": "# import file\nfrom scipy.io import wavfile\nrate,data= wavfile.read('xmit-signal.wav')  # 16 bit data from transmitter\nprint 'rate =', rate\nprint 'data =', data\nlength = np.size(data)\nprint 'length  = ', length\nk = np.linspace(0,length-1,length)\n\n####################\n# parameters used:\ndt = 1.0/(44.1*16)*1e-3  # sample period\nprint 'Ts =', dt\ntime = dt * np.linspace(0,length-1,length)\nsignal = np.zeros(length)\nomega_c = 2.0 * np.pi * 3e5\nomega_d = 2.0 * np.pi * 3.16e5  # use channel spacing of 16 kHz", "outputs": [{"output_type": "stream", "name": "stdout", "text": "rate = 44100\ndata = [ -837   414   -10 ..., -1665  1308  -870]\nlength  =  4194304\nTs = 1.41723356009e-06\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"source": "Need to specify $k_{min}$, $k_{max}$, $k_{c}$, $k_{d}$ parameters in next cell.", "cell_type": "markdown", "metadata": {}}, {"execution_count": 23, "cell_type": "code", "source": "##################\n## PARAMETERS TO BE DETERMINED\n\nkc = np.int(length*omega_c/(2*np.pi/dt)) # CHANGE THIS\nkd = np.int(length*omega_d/(2*np.pi/dt)) # change this\nprint 'k at wc=', kc\nprint 'k at wd=', kd\n\nk_min = 48000  # change this value\nk_max = 3*48000  # kc+full width of omega_d channel", "outputs": [{"output_type": "stream", "name": "stdout", "text": "k at wc= 1783292\nk at wd= 1878401\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 24, "cell_type": "code", "source": "# plot FFT of modulated signal near carrier frequency\nkcarrier = kc\nY = np.fft.fft(data)  \nsetup_graph(title='FFT of input data', x_label='$k$', y_label='$Y[k]$', fig_size=(6,3))\n_ = plt.plot(k[kcarrier-k_min:kcarrier+k_max],Y[kcarrier-k_min:kcarrier+k_max])", "outputs": [{"output_type": "display_data", "data": {"image/png": 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"text/plain": "<matplotlib.figure.Figure at 0xa2273c8>"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"source": "Specify digital low pass filter $H[k]$ with cutoff of 8 kHz", "cell_type": "markdown", "metadata": {}}, {"execution_count": 26, "cell_type": "code", "source": "# specify low pass filter\nH = np.zeros(length)\nk_cutoff =  np.int(length*8.00e3*dt)\nprint 'reconstruction k_cutoff =', k_cutoff\n# need hanning window to keep from ringing \nH[0:k_cutoff+1]=16\nH[length-k_cutoff:length]=16 # setup low pass filter with high and low", "outputs": [{"output_type": "stream", "name": "stdout", "text": "reconstruction k_cutoff = 47554\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"source": "In the next cell enter code for calculating recovered signals s1[n], s2[n], s3[n], s4[n]", "cell_type": "markdown", "metadata": {}}, {"execution_count": 27, "cell_type": "code", "source": "# code here to extract s1....s4 from ``data''\ntime = dt * np.linspace(0,length-1,length)\ncoswc = np.cos(omega_c*time) \ncoswd = np.cos(omega_d*time) \nsinwc = np.sin(omega_c*time) \nsinwd = np.sin(omega_d*time) \nprint 'cos/sin setup done'\n\n# convert to baseband then filter\nsig1 = np.multiply(coswc,data)\nsig2 = np.multiply(sinwc,data)\nsig3 = np.multiply(coswd,data)\nsig4 = np.multiply(sinwd,data)\nprint 'convert to baseband'", "outputs": [{"output_type": "stream", "name": "stdout", "text": "cos/sin setup done\nconvert to baseband\n"}], "metadata": {"scrolled": true, "collapsed": false, "trusted": true}}, {"execution_count": 28, "cell_type": "code", "source": "# perform filtering and write data\n#low pass first channel\nSig1 = np.fft.fft(sig1)       \nY = np.multiply(Sig1,H)\ns1 = np.fft.ifft(Y)\n\nSig2 = np.fft.fft(sig2)       \nY = np.multiply(Sig2,H)\ns2 = np.fft.ifft(Y)\n\nSig3 = np.fft.fft(sig3)       \nY = np.multiply(Sig3,H)\ns3 = np.fft.ifft(Y)\n\nSig4 = np.fft.fft(sig4)       \nY = np.multiply(Sig4,H)\ns4 = np.fft.ifft(Y)", "outputs": [], "metadata": {"collapsed": true, "trusted": true}}, {"execution_count": 29, "cell_type": "code", "source": "# this cell writes all data for you, and plots S1[k]\nwavwrite('sig1.wav',s1,length)\nwavwrite('sig2.wav',s2,length)\nwavwrite('sig3.wav',s3,length)\nwavwrite('sig4.wav',s4,length)", "outputs": [{"output_type": "stream", "name": "stdout", "text": "wrote file sig1.wav\nwrote file sig2.wav\nwrote file sig3.wav\nwrote file sig4.wav\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 30, "cell_type": "code", "source": "# plot FFT of s1\nSig1 = np.fft.fft(s1)   \nsetup_graph(title='FFT of s1', x_label='$k$', y_label='$S1[k]$', fig_size=(12,3))\nplt.subplot(1,2,1)\n_ = plt.plot(k[0:2*k_cutoff],Sig1.real[0:2*k_cutoff],'b')\nylabel('real')\nplt.subplot(1,2,2)\n_ = plt.plot(k[0:2*k_cutoff],Sig1.imag[0:2*k_cutoff],'g')\nylabel('Imag')\nxlabel('k')", "outputs": [{"execution_count": 30, "output_type": "execute_result", "data": {"text/plain": "<matplotlib.text.Text at 0xa49f2b0>"}, "metadata": {}}, {"output_type": "display_data", "data": {"image/png": 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