Question

Consider an LTI system whose frequency response is undesirable; the distorting system function is given as:...

Consider an LTI system whose frequency response is undesirable; the distorting system function is given as:

Hdz=(1-0.8ej0.4πz-1)(1-0.8e-j0.4πz-1)(1-1.5ej0.6πz-1)(1-1.5e-j0.6πz-1)

Assume the distorting function is both causal and stable. Design and examine compensation system Hc(z) such that when a signal sn is transmitted through this communication channel then perfect compensation is achieved i.e. scn=sn.

b)   Determine the impulse response h[n] by using the inverse Z transform.

Hz=log1+az-1+2Z-5,             z>a

c) For what value of a will be the impulse response both stable and causal? Explain your answer.

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