申論題

 1. (Total=15%) Fig. 1 shows a series of operations that are used to separate random processes into different frequency regions. The input random process x(t) is Gaussian and white with a power spectral density function of Sx(f) = 2.

 

Fig 1. Problem 1.
 The system functions of the various linear filters are as follows
We developed expressions that relate the various random processes that are inputs and outputs to linear filters. For example, recall that

Use the above properties, your knowledge of Fourier transforms, and your general knowledge of the properties of random processes to answer the following  questions.