Consider the linear system described by the difference equation
y(n) = 0.8y(n – 1) + x(n) + x(n –...

Question

Consider the linear system described by the difference equation
y(n) = 0.8y(n – 1) + x(n) + x(n – 1)
Where x(n) is a wide-sense stationary random process with zero mean and autocorrelation
?xx(m) = (1/2)|m|
(a) Determine the power density spectrum of the output y(n).
(b) Determine the autocorrelation ?yy(m) of the output.
(c) Determine the variance s2y of the output.

Robert · Accepted Answer

(a) 
 
     
 
 
 
2
1
1
1
2 2
2 2
2
2
1
1 0.8
1 1
           
1 0.8 1 0.8
cos
           4
1.64 1.6cos2
1
2
1
 
2
0.75
                 
1.

Consider the linear system described by the difference equation y(n) = 0.8y(n – 1) + x(n) + x(n – 1) Where x(n) is a wide-sense stationary random process with zero mean and autocorrelation ?xx(m) =...

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