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Consider an LTI system subjected to a wide-sense stationary input {x(n)}, which is a white noise sequence. The cross-correlation ϕx[m] between the input x(n), and output y(n) is:
Where  and h[⋅] is the impulse response.
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider an LTI system subjected to a wide-sense stationary input {x(n...
The cross-correlation function between the input and output processes is given by:
Rxy (t1, t2) = E{X(t1) Y*(t2)}

∴ The output cross-correlation between the input and the output is the convolution of the autocorrelation function of the input with the conjugate of the impulse response of the system.
Analysis:
Given the autocorrelation of the input wide-sense stationary signal as:

The cross-correlation will be:
ϕx[m] = ϕxx [m] * h[⋅]

Since x(n) * δ(n) = x(n)
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