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    % MATLAB script for Illustrative Problem 2.9.
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 over ten 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); end; % Note that Y(n) means Y(n-1).
   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; 
   echo off ;
end;
echo on ;
Rxav=Rxav/10;
Ryav=Ryav/10;
Sxav=Sxav/10;
Syav=Syav/10;
% Plotting commands follow