Suppose we wanted to generate the random process whose PSD is given in Exercise 12.8 using the

Question:

Suppose we wanted to generate the random process whose PSD is given in Exercise 12.8 using the time domain method discussed in Section 12.2.2.
(a) Find the transfer function of the analog filter which will produce the desired output PSD when the input is a zero- mean, white Gaussian random process.
(b) Use a bilinear transformation to convert the analog filter to a digital filter.
(c) What is the approximate duration of the impulse response of the digital filter if the 3- dB frequency of the random process is f3 = 1kHZ.