Question

Which of the following relation is true?

(a) ryx(l)=h(l)*ryy(l)

(b) rxy(l)=h(l)*rxx(l)

(c) ryx(l)=h(l)*rxx(l)

(d) none of the mentioned

The question was asked during an internship interview.

The doubt is from Correlation of Discrete Time Signals in division Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Correct answer is (c) ryx(l)=h(l)*rxx(l)

The best I can explain: Let x(n) be the input signal and y(n) be the output signal with impulse response h(n).

We know that y(n)=x(n)*h(n)=\(\sum_{k=-\infty}^{\infty} x(k)h(n-k)\)

The cross correlation between the input signal and output signal is

ryx(l)=y(l)*x(-l)=h(l)*[x(l)*x(-l)]=h(l)*rxx(l).