Monson H. Hayes Statistical Digital Signal Processing Problem C3.3

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Monson H. Hayes statistical Digital Signal Processing Problem C3.3 (Chapter 3 Computer Exercise): In this exercise we will look at how accurately the sample autocorrelation is in estimating the autocorrelation of white noise. The full problem is given below:

%MATLAB Code for the above problem
clc;
clear;
close all;
m = 0;
v = 1;
x = m + sqrt(v) .* randn(1000,1); % Generates 1000 samples of zero mean, m=0 and unit variance, v=1
rxb = autocorr(x,100);
[acf,lags] = autocorr(x); %returns the lag numbers that MATLAB uses to compute acf

for k = 1:100
    for m = 1:9
        for n = 1:99
      rx(k) = (1/1000) * sum(x(n+100*m) * x(n-k+100*m));    %segment white noise sequence into 10 d/t sequences
        end
    end
end

xd = m + sqrt(v) .* randn(10000,1);
rxd = autocorr(xd,100);

subplot(4,1,1),stem(x);
title('1000 Samples of zero mean unit variance white Gaussian noise');
ylabel('x(n)');
xlabel('n');
subplot(4,1,2),autocorr(x,'NumLags',100);
subplot(4,1,3),autocorr(rx,'NumLags',99);
subplot(4,1,4),autocorr(xd,'NumLags',100);

Output image of the problem

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