Question

If x(n) is the input signal of a system with impulse response h(n) and y(n) is the output signal, then the auto correlation of the signal y(n) is?

(a) rxx(l)*rhh(l)

(b) rhh(l)*rxx(l)

(c) rxy(l)*rhh(l)

(d) ryx(l)*rhh(l)

I have been asked this question during an interview.

The question is from Correlation of Discrete Time Signals topic in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Right option is (b) rhh(l)*rxx(l)

To explain I would say: ryy(l)=y(l)*y(-l)

=[h(l)*x(l)]*[h(-l)*x(-l)]

=[h(l)*h(-l)]*[x(l)*x(-l)]

=rhh(l)*rxx(l).