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 ${{\rm{\Phi }}_{xx}}\left[ m \right] = \sigma _x^2\delta \left[ m \right]$ and h[⋅] is the impulse response.

Question

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 ${{\rm{\Phi }}_{xx}}\left[ m \right] = \sigma _x^2\delta \left[ m \right]$ and h[⋅] is the impulse response.

TuteeHUB · Accepted Answer

${\sigma _x}h\left[ m \right]$

TuteeHUB · Answer

$\sigma _x^2h\left[ m \right]$

TuteeHUB · Answer

$\frac{{\sigma _x^2}}{2}h\left[ m \right]$

TuteeHUB · Answer

$\frac{{{\sigma _x}}}{2}h\left[ m \right]$

1.	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 \({{\rm{\Phi }}_{xx}}\left[ m \right] = \sigma _x^2\delta \left[ m \right]\) and h[⋅] is the impulse response.
A.	\(\sigma _x^2h\left[ m \right]\)
B.	\({\sigma _x}h\left[ m \right]\)
C.	\(\frac{{\sigma _x^2}}{2}h\left[ m \right]\)
D.	\(\frac{{{\sigma _x}}}{2}h\left[ m \right]\)
Answer» B. \({\sigma _x}h\left[ m \right]\)

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 \({{\rm{\Phi }}_{xx}}\left[ m \right] = \sigma _x^2\delta \left[ m \right]\) and h[⋅] is the impulse response.

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