Advanced MATLAB (for Electrical Engineers) Day 2

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Advanced MATLAB(for Electrical Engineers)Day 2

• Instructor Kamran Arshad
• EE Club, KFUPM
• 28 March 2004
• KFUPM

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Line of Action

• Today course follows as
• General Communication Concepts
• Fourier Transform of signals
• Finding autocorrelation and PSD of signals
• Generation of Gaussian random variables
• Amplitude Modulation
• Frequency Modulation
• Simulation of a simple binary data transmission
  scheme (Digital communication)

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Why we study these topics only ?

• Fourier analysis is important ----we are
  interested in spectrum of signals.
• Gaussian random variables --- we model noise
  normally as WGN.
• In statistical analysis, autocorrelation and PSD
  are most important parameters.
• AM and FM are most popular analog transmission
  techniques

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Fourier Transform

• Extension of Fourier series for non periodic
  signals
• Fourier transform of a time domain signal x(t) is
  given by
• In MATLAB we use function fft and fftshift.
• Type on your command prompt help fft and help
  fftshift

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Problem !!!

• Calculate and plot the spectrum of an audio
  signal.
• Plot signal in time domain as well as signal in
  frequency domain (spectrum) in one figure window.
• Use MATLAB functions fft, fftshift, subplot and
  plot.

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MATLAB Code

• clc To clear Screen
• clear Clear all previousy stored
  variables
• close all Close all open windows
• Load data file (audio file)
• This command load variables fs, t and signal m
• load Audio_Signal.mat
• Plot the signal in time domain
• subplot(211),plot(t,m)
• title('Audio Signal in time domain')
• xlabel('Time (seconds)')
• Calculating the Fourier Transform of signal
• Mfftshift(fft(m))
• Magnitude Spectrum
• Mabs(M)
• MM/max(M)

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Spectrum of Audio Signal
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Gaussian Random Variables

• Random processes are an integral part of any
  communication system.
• Often used in practice to simulate effect of
  noise or noiselike signals.
• MATLAB library have several random number
  generators like rand and randn
• See help of these two functions
• There are many methods of generating random
  variables, I choose one of them.

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On command window .

• On your command prompt type the following lines
• var1
• var2
• for i110000
• var1(i),var2(i)g_rand_generator
• end
• subplot(121),hist(var1,1000)
• subplot(122),hist(var2,1000)

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MATLAB Code

• function GRV1,GRV2 g_rand_generator(m,sgma)
• r_rand_generator generates tow independant
  gaussian random variables
• of mean m and variance sgma. By default value
  of m is 0 and sgma is 1.
• If no input argument is given assume these
  values
• if nargin 0
• m0 sgma 1
• end
• Generate a uniform random variable in the range
  0 and 1
• u rand
• Generate a Rayleigh distributed random variable
• z sgma(sqrt(2log(1/(1-u))))
• Another uniform random variable in the range 0
  and 1
• u rand
• Gaussian Random Variables

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Distribution of Gaussian Random Variables
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