Lab Primer Through Matlab Pdf

Getting Started with MATLAB. The name MATLAB stands for matrix laboratory. MATLAB was originally written to provide easy access to matrix software developed by the LINPACK and EISPACK projects. Today, MATLAB engines incorporate the LAPACK. Form and in PDF format. MATLAB Online Help To view the online documentation. Written for undergraduate students, Lab Primer Through MATLAB presents a number of techniques which help students carry out various experiments in the fields of digital signal processing, digital image processing, digital signal processor, and digital communication. A step-wise discussion of the programming procedure using MATLAB® has been carried out in this book. Laplace Transforms with MATLAB a. Calculate the Laplace Transform using Matlab Calculating the Laplace F(s) transform of a function f(t) is quite simple in Matlab.First you need to specify that the variable t and s are symbolic ones.

  1. Lab Primer Through Matlab Pdf Free
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Generation of random variables with required probability distribution characteristic is of paramount importance in simulating a communication system. Let’s see how we can generate a simple random variable, estimate and plot the probability density function (PDF) from the generated data and then match it with the intended theoretical PDF. Normal random variable is considered here for illustration. Other types of random variables like uniform, Bernoulli, binomial, Chi-squared, Nakagami-m are illustrated in the next section.

Step 1: Create the random variable

A survey of commonly used fundamental methods to generate a given random variable is given in [1]. For this demonstration, we will consider the normal random variable with the following parameters : (mu) – mean and (sigma ) – standard deviation. First generate a vector of randomly distributed random numbers of sufficient length (say 100000) with some valid values for (mu) and (sigma ) . There are more than one way to generate this. Some of them are given below

This article is part of the book Wireless Communication Systems in Matlab, ISBN: 978-1720114352 available in ebook (PDF) format (click here) and Paperback (hardcopy) format (click here).

● Method 1: Using the in-built random function (requires statistics toolbox)

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L=100000;%length of the random vector

● Method 2: Using randn function that generates normally distributed random numbers having (mu = 0) and (sigma) = 1

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histogram(R,'Normalization','pdf');%plot estimated pdf from the generated data
X=-4:0.1:4;%range of x to compute the theoretical pdf
fx_theory=pdf('Normal',X,mu,sigma);%theoretical normal probability density
holdon;plot(X,fx_theory,'r');%plot computed theoretical PDF
title('Probability Density Function');xlabel('values - x');ylabel('pdf - f(x)');axistight;

However, if you do not have Matlab version that was released before R2014b, use the ‘hist’ function and get the histogram frequency counts ((f)) and the bin-centers ((x)). Using these data, normalize the frequency counts using the overall area under the histogram. Plot this normalized histogram and overlay the theoretical PDF for the chosen parameters.

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%For those who don't have access to 'histogram' function
%get un-normalized values from hist function with same number of bins as histogram function
[f,x]=hist(R,numBins);%use hist function and get unnormalized values
figure;plot(x,f/trapz(x,f),'b-*');%plot normalized histogram from the generated data
X=-4:0.1:4;%range of x to compute the theoretical pdf
fx_theory=pdf('Normal',X,mu,sigma);%theoretical normal probability density
holdon;plot(X,fx_theory,'r');%plot computed theoretical PDF
title('Probability Density Function');xlabel('values - x');ylabel('pdf - f(x)');axistight;

Step 3: Theoretical PDF:

The given code snippets above, already include the command to plot the theoretical PDF by using the ‘pdf’ function in Matlab. It you do not have access to this function, you could use the following equation for computing the theoretical PDF

$$ f_X(x) = frac{1}{sqrt{2 pi sigma^2}} exp left[ -frac{left(x-muright)^2}{2 sigma^2} right]
$$

The code snippet for that purpose is given next.

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X=-4:0.1:4;%range of x to compute the theoretical pdf
fx_theory=1/sqrt(2*pi*sigma^2)*exp(-0.5*(X-mu).^2./sigma^2);
plot(X,fx_theory,'k');%plot computed theoretical PDF

Note: The functions – ‘random’ and ‘pdf’ , requires statistics toolbox.

References:

[1] John Mount, ‘Six Fundamental Methods to Generate a Random Variable’, January 20, 2012

[2] Thomas, D. B., Luk. W., Leong, P. H. W., and Villasenor, J. D. 2007. Gaussian random number generators. ACM Comput. Surv. 39, 4, Article 11 (October 2007), 38 pages DOI = 10.1145/1287620.1287622 http://doi.acm.org/10.1145/1287620.1287622

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[3] Matlab documentation for various functions used : random, pdf, histogram, hist

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Lab Primer Through Matlab Pdf Free

Primer

Topics in this chapter

Random Variables - Simulating Probabilistic Systems
● Introduction
● Plotting the estimated PDF
● Univariate random variables
□ Uniform random variable
□ Bernoulli random variable
□ Binomial random variable
□ Exponential random variable
□ Poisson process
□ Gaussian random variable
□ Chi-squared random variable
□ Non-central Chi-Squared random variable
□ Chi distributed random variable
□ Rayleigh random variable
□ Ricean random variable
□ Nakagami-m distributed random variable
● Central limit theorem - a demonstration
● Generating correlated random variables
□ Generating two sequences of correlated random variables
□ Generating multiple sequences of correlated random variables using Cholesky decomposition
● Generating correlated Gaussian sequences
□ Spectral factorization method
□ Auto-Regressive (AR) model
Lab Primer Through Matlab Pdf

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