7.8. Signal Processing

In this section we examine several input-output relationships for linear systems for the case in which the system input, and consequently the system output, is random. We have interest in the following basic results:

• Relationship between the mean of the system input and the system output

• Relationship between the variance of the system input and the system output

• Input-output cross-correlation

• Relationship between the autocorrelation and PSD of the system input and the system output