Question

Please show all your working

7. Consider the problem of generating samples of a lowpass random process by passing a while noise sequence Xn through a lowpass filter. The ipu s a sequenceof unifornly distributed random variable on the interval (. The lowpass filter has the impulse h(n)-(0.9)", n > 0 0,n<0 and is characterized by the input-output recursive (difference) equation (a) Write a MATLAB script to compute the output sequence Y (b) Plot the autocorrelation functions Rx(m) and Ry (m) (c) Plot the power spectra Sx(f) and Sy (f)

Answer 1

(a) f=100;
fs=1000;
n=[1:1000]*f/fs;
u=ones(n,0);
X(n)=2*cos(0.5*pi*n).u(n);
Y(n)=0.9Yn-1+Xn;

(b)autocorelated grap between Rx(m) and Ry(m) are as follows

1.2 0.8 0.6 0.4 0.2 0.2 5 10 15 2025 30 35 40 45 50

c)power spectral grap:between Sx(f) and Sy(f) are as follows:

15 10 -5 -10 -15 20 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5