engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Random Processes Transmission of Random Processes Through Linear Systems
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.
1
\(\sigma _x^2h\left[ m \right]\)
2
\({\sigma _x}h\left[ m \right]\)
3
\(\frac{{\sigma _x^2}}{2}h\left[ m \right]\)
4
\(\frac{{{\sigma _x}}}{2}h\left[ m \right]\)