{ "metadata": { "name": "", "signature": "sha256:28abd0d3a1dcbcad5611582428a6399778269bb6bf82f6c15b42c9e36f9e8ee5" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 3, Radio Communication Via a Computer Interface, Part II Digital Communication\n", "\n", "## Analog Modulation\n", "In analog communications we encode contiuous valued signals on top of a carrier frequency. Information can be encoded in the amplitude , for example: amplitude modulation (AM) or single sideband (SSB). It can also be encoded in the phase, for example: phase modulation or frequency modulation or encoded in both phase and amplitude. Once of the issues with analog modulation is that you can never get the signal you are transmitting exactly recovered. It will always be contaminated by system imperfections, noise and other deviations. \n", "At the same time, analog communication offeres simple implementations as well as robustness because signals often degrade gracefully and information can still be extracted from them even with severe interferences and low signal to noise ratio.\n", "\n", "## Digital Modulation\n", "In contrast, in digital communications we transmit quantaized digital data. Because the information is digital, this form of communications offers the advantage of a perfect reproduction of the transmitted signal. Much like analog communications, digital data can be encoded in many different ways using phase, amplitude and frequency. It can be encoded using a binary stream in which '0's and '1's are transmitted in each time interval. It can also be encoded with M-ary symbols, in which higher order symbols (for example 4-ary 0,1,2,3) are transmitted in each time interval. \n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Import functions and libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pyaudio\n", "import Queue\n", "import threading,time\n", "import sys\n", "\n", "from numpy import pi\n", "from numpy import sin\n", "from numpy import zeros\n", "from numpy import r_\n", "from scipy import signal\n", "from scipy import integrate\n", "\n", "import threading,time\n", "import multiprocessing\n", "\n", "from rtlsdr import RtlSdr\n", "from numpy import mean\n", "from numpy import power\n", "from numpy.fft import fft\n", "from numpy.fft import fftshift\n", "from numpy.fft import ifft\n", "from numpy.fft import ifftshift\n", "import bitarray\n", "from scipy.io.wavfile import read as wavread\n", "\n", "\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 78 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot an image of the spectrogram y, with the axis labeled with time tl,\n", "# and frequency fl\n", "#\n", "# t_range -- time axis label, nt samples\n", "# f_range -- frequency axis label, nf samples\n", "# y -- spectrogram, nf by nt array\n", "# dbf -- Dynamic range of the spect\n", "\n", "def sg_plot( t_range, f_range, y, dbf = 60) :\n", " eps = 1e-3\n", " \n", " # find maximum\n", " y_max = abs(y).max()\n", " \n", " # compute 20*log magnitude, scaled to the max\n", " y_log = 20.0 * np.log10( abs( y ) / y_max + eps )\n", " \n", " fig=figure(figsize=(15,6))\n", " \n", " plt.imshow( np.flipud( 64.0*(y_log + dbf)/dbf ), extent= t_range + f_range ,cmap=plt.cm.gray, aspect='auto')\n", " plt.xlabel('Time, s')\n", " plt.ylabel('Frequency, Hz')\n", " plt.tight_layout()\n", "\n", "\n", "def myspectrogram_hann_ovlp(x, m, fs, fc,dbf = 60):\n", " # Plot the spectrogram of x.\n", " # First take the original signal x and split it into blocks of length m\n", " # This corresponds to using a rectangular window %\n", " \n", " \n", " isreal_bool = isreal(x).all()\n", " \n", " # pad x up to a multiple of m \n", " lx = len(x);\n", " nt = (lx + m - 1) // m\n", " x = append(x,zeros(-lx+nt*m))\n", " x = x.reshape((m/2,nt*2), order='F')\n", " x = concatenate((x,x),axis=0)\n", " x = x.reshape((m*nt*2,1),order='F')\n", " x = x[r_[m//2:len(x),ones(m//2)*(len(x)-1)].astype(int)].reshape((m,nt*2),order='F')\n", " \n", " \n", " xmw = x * hanning(m)[:,None];\n", " \n", " \n", " # frequency index\n", " t_range = [0.0, lx / fs]\n", " \n", " if isreal_bool:\n", " f_range = [ fc, fs / 2.0 + fc]\n", " xmf = np.fft.fft(xmw,len(xmw),axis=0)\n", " sg_plot(t_range, f_range, xmf[0:m/2,:],dbf=dbf)\n", " print 1\n", " else:\n", " f_range = [-fs / 2.0 + fc, fs / 2.0 + fc]\n", " xmf = np.fft.fftshift( np.fft.fft( xmw ,len(xmw),axis=0), axes=0 )\n", " sg_plot(t_range, f_range, xmf,dbf = dbf)\n", " \n", " return t_range, f_range, xmf" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 79 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example of Different Digital Modulations:\n", "\n", "In the following sections we will consider signals with a symbol-rate of 300 bauds (300b/s) with a carrier frequency of 1800Hz and a sampling rate of 44100. Each bit will correspond to 44100/300 = 147 samples. The carrier frequency was chosen such that there exactly 6 cycles in a bit -- this is useful for the phase-based modulation schemes. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "fs = 44100 # sampling rate\n", "baud = 300 # symbol rate\n", "Nbits = 10 # number of bits\n", "Ns = fs/baud\n", "N = Nbits * Ns\n", "f0 = 1800\n", "bits = randn(Nbits,1) > 0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 80 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Amplitude-Shift-Keying (ASK) or On-Off Keying (OOK) \n", "ASK/OOK encodes digital data in the amplitude of the carrier, $M(t)\\cos(2\\pi f_0t)$ where $M(t) = \\{0~or~1\\}$ for binary data. We saw such an example in the ADS-B mode S lab previously. M-ary digital data can also be encoded in the amplitude by dividing the the amplitude into more segments. For example $M(r) = \\{0~or~0.33~or~0.66~or~1.0\\}$ for a 4-ary symbol\n", "\n", "Here's an example of an OOK signal:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(seed=1)\n", "bits = randn(Nbits,1) > 0\n", "M = np.tile(bits,(1,Ns))\n", "t = r_[0.0:N]/fs\n", "OOK = M.ravel()*sin(2*pi*f0*t)\n", "\n", "fig = figure(figsize = (16,4))\n", "plot(t,OOK)\n", "xlabel('time [s]')\n", "title('OOK signal of the sequence:'+ np.array2string(transpose(np.uint8(bits))))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 81, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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9NDMDkH5K4oRTwWx6ikN5efj1pKbsqaYZB7WpUwNBCClOdPRNtWZWV09lbKrq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\n9g4M3L6dfkrcI1bBbE0NsGaNvRQH356tYLamxtsNUNlJ6Nb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"text": [ "" ] } ], "prompt_number": 81 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The approach of using OOK/ASK as above is not ideal. We can see this by plotting the spectrum\n", "\n", "* Compute the spectrum of the above ook signal using FFT, and plot its magnitude. \n", "* Comment on the spectrum. What is the issue that may arise if one would like to transmit at nearby frequencies?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 81 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of using rectangular pulses, we can use shaped pulses which have more narrowband frequency response. For example, we could use sinc based pulses that would result in bandlimited spectrum. Of course it is not practical to use a sinc, since it is infinite in length. Instead we can use a truncated (windowed) sinc pulses with certain time bandwidth (TBW) product that would have a finite length as well as narrow bandness. \n", "\n", "\n", "Thinking in terms of the time-bandwidth product (TBW), the TBW of a rectangular pulse is 1, so for a symbol length of 1/300 seconds we get a bandwidth of 300 Hz (The the main lobe full width at half the maximum) but lots of ripple. We could use a TBW = 2 pulse (like a hamming window or higher order pulses. \n", "\n", "* Using the random bit sequence chosen above, generate a new sequence with either zero or discrete impulses spaced fs/baud samples apart. For example a sequence of 1010 would have an impulse at position 0, an impulse at position 294 and zeros elsewhere\n", "* Generate a TBW = 4 windowed sinc pulse with zero-crossing occuring every 147 samples. \n", "* Convolve the sinc with the impulse train to generate a sinc OOK/ASK signal. \n", "* modulate the result to 1800Hz\n", "* Plot the signal and its spectrum\n", "* Comment on the separation between on and off.... what happened? Comment on the spectrum." ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 81 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Answer:\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Phase-shift-keying (PSK) \n", "PSK encodes digital data in the phase of the signal. For example, Binary PSK (BPSK) sends a stream of '0's and '1's by alternating the sign of the carrier in each bit period: $Real \\left \\{ e^{\\pi M(t)}\\cos(2\\pi f_0t) \\right \\}$, where $M(t)$ is a signal of $0~or~1$ corresponding to '0's and '1's. The RDS subcarrier in FM radio is BPSK encoded. An M-ary symbol can be transmitted by MPSK in which $M(t)$ are broken to smaller intervals. For example in 4 PSK (QPSK) 0,1,2,4 are encoded in $M(t) = \\{0~or~0.5~or~1~or~1.5\\}$. It could also be encoded in a $45^\\circ$ rotated constellation $M(t) = \\{0.25~or~0.75~or~1.25~or~1.75\\}$ \n", "\n", "Here's an example of a BPSK signal:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(seed=1)\n", "bits = randn(Nbits,1) > 0 \n", "M = np.tile(bits*2-1,(1,Ns))\n", "t = r_[0.0:N]/fs\n", "BPSK = M.ravel()*sin(2*pi*f0*t)\n", "\n", "fig = figure(figsize = (16,4))\n", "plot(t,BPSK)\n", "xlabel('time [s]')\n", "title('BPSK signal of the sequence:'+ np.array2string(transpose(np.uint8(bits))))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 82, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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szqk4/zRunL7x1dERBbkw+pRTv7mkTwEGgwcYnrrCG0q8rKBLZyfOSejoiHRt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"text": [ "" ] } ], "prompt_number": 82 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the advantages od PSK is that the envelope of the signal is constant. This means that we don't have to use linear amplifiers (also called class A) in order to amplify the signal for transmission. Instead we can use the much more efficient non-linear amplifiers (class C). However, the problem is of course that the phase has a discontinuity. This will have an effect on the spectrum. \n", "\n", "* Compute the spectrum of the above BPSK signal. Comment on the spectrum" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 82 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the same \"trick\" as before and shape the pulses with a windowed sinc function. \n", "\n", "* Repeat the procedure for the case of BPSK similarly to the shaped ASK/OOK as before. However instead of a zero-one pulse train use a $\\pm 1$ train to get the changes in phase. \n", "* What did we win and what did we lose? Comment on the spectrum the symbol leakage and the envelope of the signal." ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 82 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Quadrature-Amplitude-Modulation (QAM)\n", "QAM encodes M-arry digital data in both the amplitude and phase, i.e., $Real \\left \\{ M(t)\\cos(2\\pi f_0t) \\right \\}$ where M(t) have an amplitude and phase that divides the complex plane into M segments. \n", "QAM is heavily used in cable TV and modems. You can see constellations of QAM-16 to QAM-256 which break the complex plane to $4\\times 4$ and $16\\times 16$ grids. \n", " \n", "Here's an image of the constallation of QAM-16:\n", "
\"qam16\"
\n", "
Figure 1: QAM-16 Constallation
\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#code = { 2: -2+2j, 6: -1+2j, 14: 1+2j, 10: 2+2j,\n", "# 3: -2+1j, 7: -1-1j, 15: 1+1j, 11: 2+1j,\n", "# 1: -2-1j, 5: -1-1j, 13: 1-1j, 9: 2-1j,\n", "# 0: -2-2j, 4: -1-2j, 12: 1-2j, 8: 2-2j}\n", "Nbits = 16 # number of bits\n", "N = Nbits * Ns\n", "code = np.array((-2-2j, -2-1j,-2+2j,-2+1j,-1-2j,-1-1j,-1+2j,-1+1j,+2-2j,+2-1j,+2+2j,+2+1j,1-2j,+1-1j,1+2j,1+1j))/2\n", "np.random.seed(seed=1)\n", "bits = np.int16(rand(Nbits,1)*16) \n", "M = np.tile(code[bits],(1,Ns))\n", "t = r_[0.0:N]/fs\n", "\n", "# these are two ways of producing the same result:\n", "#QAM = (M.real.ravel()*cos(2*pi*f0*t) - M.imag.ravel()*sin(2*pi*f0*t))/2/sqrt(2)\n", "QAM = real(M.ravel()*exp(1j*2*pi*f0*t))/sqrt(2)/2\n", "fig = figure(figsize = (16,4))\n", "plot(t,QAM.real)\n", "xlabel('time [s]')\n", "title(\"QAM=16 of the sequence:\"+ np.array2string(transpose(bits)))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 83, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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o3GpvF+8fNMhMg3NgcxOswDIYDAaDwWAoIL2flIBMeWApGqZcQSnImxTYoiIO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\n83/XQ5wkjfr6nlOPdeUSLlf52HhgTXKM7pnQvcYmjDku0wHh3lEgPLw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21hDiUH17jXS/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fwyEFI0Wd7RmteArfTYIvVF7sc7Y8YMPPbYY2P+f968eXjooYcAAKeddhqefvrp/NIR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\nePTRR7F27dpx/w2ke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"text": [ "" ] } ], "prompt_number": 83 }, { "cell_type": "markdown", "metadata": {}, "source": [ "QAM is a very efficient way to use the amplitude as well as the phase to encode M-arry symbols. \n", "\n", "* Compute the spectrum of the above QAM 16 signal. \n", "* Repeat the same for shaped TBW=4 pulses. \n", "* Is the bandwidth much different than the binary sequences? What is the bitrate improvement per bandwidth you get?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 83 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Frequency-Shift-Keying (FSK)\n", "FSK encodes digital data in the frequency of the carrier, i.e., $\\cos \\left(2\\pi (f_0 + M(t)\\Delta f)t\\right)$. For binary FSK (BFSK), $M(t) =\\{1~or~-1\\}$. In M-arry FSK (MFSK) the frequency band can be broken to more segments. Again, much like PSK, FSK has also a constant envelope which makes it ideal for use with efficient non-linear amplifiers. \n", "\n", "The choise of frequencies has a huge impact on our ability to demodulate the signal as well as the bandwidth of it. For example, we would like the frequencies to be orthogonal over a bit period so when detected using correlation we will ge the maximum difference between the results. We would also like the phase to be continuous for the sidelobes to decay rapidly and not interfere with nearby channels. \n", "\n", "For example, the choice of frequencies of 1200Hz and 2400Hz below for a bitrate of 300 baud results in 4 and 8 cycles per bit period respectively. The outcome is a smooth phase and orthogonal frequencies. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(seed=1)\n", "Nbits = 10\n", "N = Nbits * Ns\n", "bits = randn(Nbits,1) > 0 \n", "M = np.tile(bits*2-1,(1,Ns))\n", "delta_f = 600\n", "\n", "# compute phase by integrating frequency\n", "ph = 2*pi*cumsum(f0 + M.ravel()*delta_f)/fs\n", "t = r_[0.0:N]/fs\n", "FSK = sin(ph)\n", "\n", "fig = figure(figsize = (16,4))\n", "plot(t,FSK)\n", "xlabel('time [s]')\n", "title('FSK signal of the sequence:'+ np.array2string(transpose(np.uint8(bits))))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 84, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Oe3rUeTbtjErFaa2mPuOMGTScTp+unAxpe50LOAXG9n4JPgX4zlOc+34ri1PG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\nizXvAnvTNGOq50uTFSU1hVp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U2LjPlTWKKnE+BehOT9f4tLNTfZ5aLfqsmaZXgk/nzIn+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\nFp2+GfV8Se7LO9pfqajfS0S8isYplc+i9JqmGXN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pYuogkeDePBrqSbwnE70SfNrRMdb1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"text": [ "" ] } ], "prompt_number": 84 }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Compute the spectrum of the above FSK signal. Can you see the frequencies?\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 84 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reason the frequencies are separated well is the low bit-rate.\n", "For the same choice of frequencies we can increase the baud (i.e. the bit-rate) and still get continuous phase and orthogonal frequencies. For example: with a 600 bause we will get 2 cycles for 1200Hz and 4 cycles for 2400Hz per bit period. We can continue further for 1200baud which results in 1cycle/2cycle for 1200Hz/2400Hz. \n", "\n", "Finally, the highest rate in which we can get orthogonal frequencies is 2400 baud. In that case, we will have 1/2 a cycle at 1200Hz and 1 cycle for 2400Hz. The phase will still be continuous and the frequencies orthogonal. This form of FSK modulation is also called Minimum-Shift-Keying (MSK) and is generalized to the case where the frequency difference is half the bit-rate.\n", "\n", "* What would be the choice of frequencies for a 300 baud MSK centered at 1800Hz?\n", "* Generate the MSK-300 modulation of the above signal.\n", "* Plot the signal as well as its spectrum and spectrogram For the spectrogram use 148 window (which is approximately the bit length). Comment on the bandwidth of the signal compared to the BFSK above." ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 84 }, { "cell_type": "markdown", "metadata": {}, "source": [ "MSK is a very efficient modulation with constant envelope and a narrow bandwidth. However its sidelobes are still prohibitly high for application like cellphone networks. The sidelobes can be further reduce by prefiltering the frequency transition by a smoothing filter. A very common filter is a gaussian filter. When a gaussian filter is used, the modulation is called GMSK. This is the modulation that is used for GSM networks. Much like the other modulations, filtering reduces the sidelobes, but increase the inter-symbol interference. \n", "\n", "The Gaussian filter used in GMSK is defined as:\n", "$$ h(t) = \\sqrt{\\frac{2\\pi}{\\mathrm{log} 2}} \\cdot BW \\mathrm{exp}\\left(-\\frac{2\\pi^2(BW)^2}{\\mathrm{log}2}t^2\\right) $$, \n", "where BW is determined by the time-bandwidth product (TBW) and the duration of the gaussian pulse, which is $\\frac{T_b}{TBW}$ -- where $T_b$ is the bit time-period. \n", "\n", "In the discrete case, where $f_s$ is the sampling frequency \n", "$$ h[n] = \\sqrt{\\frac{2\\pi}{\\mathrm{log} 2}} \\cdot \\frac{BW}{f_s} \\mathrm{exp}\\left(-\\frac{2\\pi^2}{\\mathrm{log}2}\\frac{(BW)^2}{f_s^2}n^2\\right) $$, \n", "\n", "* Generate a TBW=0.5 gaussian filter over a 2bit time period. What is the bandwitdh?\n", "* Plot the filter. \n", "* Filter the frequency of the MSK signal above using the gaussian filter. Integrate to generate the phase to generate the modulated signal as above. \n", "* Plot the signal and its spectrum. Comment on the result. Does the spectrum have less sidelobes? \n", "* Explain why the spectrum looks like it is and compare to the spectrogram. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 84 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Demodulation\n", "There are many ways to demodulate digital modulation schemes. Some demodulators have to be synchronized (coherent) to the phase of the signal and some are not (incoherent). The methods differ by the complexity of the implementation as well as the bit-error-rate (BER) they exhibit when noise is present. We will not cover the demodulation of all the above schemes in this lab. \n", "\n", "In the next part of the lab we will mostly focus on one modulation/demodulation schem -- AFSK, which is a form of frequency shift keying in the audio range. \n", "\n", "At the same time, you are more than welcome to use any of the above modulation schemes in your project. I will be ahppy to provide you with information how to demodulate them -- although the internet is full of information as well as communication textbooks.\n" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }