Question: Consider the following problems for LTI discrete-time systems. (a) The input and the output of a LTI discrete-time system are Find the transfer function H(z).

Consider the following problems for LTI discrete-time systems.

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

n = 0, 3 n = 0, 1 Output y[n] n = 1, 2 Input x[n] = otherwise otherwise

Find the transfer function H(z).

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

1- 0.5z -1 Н2) |z| > 0.5 1- 0.25z- -2

i. Is this system causal? Explain.

ii. Determine the impulse response of the system.

(c) The transfer function of an LTI system is

What are the values of h[0],h[1] and h[1000] of the impulse response.

n = 0, 3 n = 0, 1 Output y[n] n = 1, 2 Input x[n] = otherwise otherwise 1- 0.5z -1 Н2) |z| > 0.5 1- 0.25z- -2

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