In Problems 1.45 and 2.67, we defined and examined several of the properties and uses of...

In Problems 1.45 and 2.67, we defined and examined several of the properties and uses of correlation functions. In the current problem, we examine the properties of such functions in the frequency domain. Let x(t) and y(t) be two real signals. Then the cross-correlation function of x(t) and y(t) is defined as

(e) Let x(t) be as is illustrated in Figure P4.50, and let the LTI system impulse response be (jω) using the results of parts (a)-(d).

(f) Suppose that we are given the following Fourier transform of a function:

Find the impulse responses of two causal, stable LTI systems that have relation functions equal to Which one of these has a causal, stable inverse?