Question

7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed white The sample functions of this process is filtered according to the n( zn-1)+x(n) (5 points). Write the MATLAB code for the computation of autocorrelation of the processes X(n) and Z(n) by repeating the experiment 100 times. (5 points). b.

Answer 1

close all,
clear all,
clc,

Xn=[];
Zn=[];
for n=1:1000
Xn(n) = randn();
if(n==1), Zn(n) = Xn(n); end
if(n>1),
Zn(n) = 0.95 * (Zn(n-1) + Xn(n));
end
end
subplot(2,2,1); plot(Xn); title('Zero Mean Gaussian Distributed Random Noise')
subplot(2,2,2); plot(Zn); title('Zn = 0.95 * (Z(n-1) + xn)');
[Pxx,w] = pwelch(Xn);
subplot(2,2,3); plot(w,Pxx); title('Power Spectral Estimate for Signal Xn');

[Pxx,w] = pwelch(Zn);
subplot(2,2,4); plot(w,Pxx); title('Power Spectral Estimate for Signal Zn');

for ExpNo=1:100
Xn=[];
Zn=[];
for n=1:1000
Xn(n) = randn();
if(n==1), Zn(n) = Xn(n); end
if(n>1),
Zn(n) = (0.95 * Zn(n-1)) + Xn(n);
end
end
C_Xn = xcorr(Xn); %Auto-Correlation of Proces Xn
C_Zn = xcorr(Zn); %Auto-Correlation of Proces Zn
Covariance_Xn = cov(Xn);
Covariance_Zn = cov(Zn);
end

Zn 095 (Zn-1) + xn) Zero Mean Gaussian Distributed Random Noise 10 -E 0 100 200 300 400 500 600 700 800 900 1000 0 100 200 300 400 00600 700 800 900 1000 Power Spectral Estimate for Signal Xn Power Spectral Estimate for Signal Zn 0.7 140 120 0.6 100 0.5 80 0.3 0.2 40 20 0.5 2.5 2.5 3.5 0.5 3.5