The following problems relate to FIR and IIR systems.

(a) The input and the output of a causal LTI discrete-time system are

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Determine the impulse response h[n].

(b) The transfer function H(z)of an LTI discrete-time system has a  pole at z = 0, a double zero at z = ˆ’1 and a dc gain H(1) = 2.

i. Determine the transfer function H(z)and its region of convergence. Is this FIR or IIR filter?

ii. If the input of the LTI system is x[n] = ­(1 + cos(Ï€n/2) + ( ˆ’ 1)ⁿ) u[n], what is the steady-state  response y_ss[n]of this system?

(c) The transfer function of an LTI discrete-time system is

i. Find the poles and zeros of H(z) and indicate its region of convergence if the impulse response h[n] of the system is non-causal.

ii. Assume h[n]is causal, and find it from H(z).

iii. Determine whether the system is BIBO stable or not when the  impulse response is non-causal or causal. Explain.

Transcribed Image Text:

n < 0 Input x[n] = (-1)"u[n] _Output y[n] = {n+ 1 n = 0, 1, 2 3(-1)" n > 3 Н(2) - (z – 0.5)(z + 2)