Auto Correlation of the Output Signal

The auto correlation of a signal measures the similarity between the signal and a delayed version of itself. In this case, we are interested in finding the auto correlation of the output signal y(n), which is the result of convolving the input signal x(n) with the impulse response h(n) of a system.

Understanding the Options

Let's analyze each option to understand why option 'B' is the correct answer.

a) rxx(l)*rhh(l): This option suggests that we should multiply the auto correlation of the input signal rxx(l) with the auto correlation of the impulse response rhh(l). However, this doesn't make sense because we are interested in the auto correlation of the output signal, not the input signal or the impulse response.

b) rhh(l)*rxx(l): This option suggests that we should multiply the auto correlation of the impulse response rhh(l) with the auto correlation of the input signal rxx(l). This seems more plausible because the output signal y(n) is obtained by convolving the input signal x(n) with the impulse response h(n).

c) rxy(l)*rhh(l): This option suggests that we should multiply the cross correlation between the input signal x(n) and the output signal y(n) with the auto correlation of the impulse response rhh(l). However, this doesn't make sense because we are interested in the auto correlation of the output signal, not the cross correlation between the input and output signals.

d) ryx(l)*rhh(l): This option suggests that we should multiply the cross correlation between the output signal y(n) and the input signal x(n) with the auto correlation of the impulse response rhh(l). However, this doesn't make sense because we are interested in the auto correlation of the output signal, not the cross correlation between the input and output signals.

Conclusion

Based on the analysis of the options, it is clear that option 'B' is the correct answer. Multiplying the auto correlation of the impulse response rhh(l) with the auto correlation of the input signal rxx(l) gives us the auto correlation of the output signal y(n). This makes sense because the output signal is obtained by convolving the input signal with the impulse response. The auto correlation of the impulse response reflects the system's characteristics, while the auto correlation of the input signal represents its statistical properties.