The impulse response of a causal LTI discrete-time system is

(a) If the input of the system is a pulse x[n] = u[n] ˆ’ u[n ˆ’ 3], determine  the length of the output of the system y[n]. Graphically calculate the  output of the system y[n] as the convolution sum of x[n] and h[n].

(b) Determine the transfer function H(z) of the system. Is this system BIBO stable? Explain.

(c) Suppose you want to recover x[n] from the output y[n] by cascading a system with tranfer function  HÌ‚(z) to the given system with  transfer function H(z). What should  HÌ‚(z) be equal to? Is the cas-caded system with HÌ‚(z) as transfer function BIBO stable? Can you  guarantee recovery of the original signal x[n]? Explain.

Transcribed Image Text:

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