?? ip_02_09.m
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% MATLAB script for Illustrative Problem 9, Chapter 2.
N=1000; % The maximum value of n
M=50;
Rxav=zeros(1,M+1);
Ryav=zeros(1,M+1);
Sxav=zeros(1,M+1);
Syav=zeros(1,M+1);
for i=1:10, % take the ensemble average ove 10 realizations
X=rand(1,N)-(1/2); % Generate a uniform number sequence on (-1/2,1/2)
Y(1)=0;
for n=2:N,
Y(n) = 0.9*Y(n-1) + X(n); % note that Y(n) means Y(n-1)
end;
Rx=Rx_est(X,M); % Autocorrelation of {Xn}
Ry=Rx_est(Y,M); % Autocorrelation of {Yn}
Sx=fftshift(abs(fft(Rx))); % Power spectrum of {Xn}
Sy=fftshift(abs(fft(Ry))); % Power spectrum of {Yn}
Rxav=Rxav+Rx;
Ryav=Ryav+Ry;
Sxav=Sxav+Sx;
Syav=Syav+Sy;
end;
Rxav=Rxav/10;
Ryav=Ryav/10;
Sxav=Sxav/10;
Syav=Syav/10;
% Plotting commands follow
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