The input-output relationship of a discrete-time LTI system is given as follows yln] = 2x[n – 4] – 3x[n – 6]. a) Determine the impulse response of the system, h[n]. b) Using h[n], show that the system is causal. c) Using h[n], show that whether the system is BIBO stable or not.

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The input-output relationship of a discrete-time LTI system is given as follows
y[n] = 2x[n – 4] – 3x[n – 6].
a) Determine the impulse response of the system, h[n].
b) Using h[n], show that the system is causal.
c) Using h[n], show that whether the system is BIBO stable or not.
d) Determine the transfer function H(z). Plot pole-zero diagram. Indicate ROC.
e) Using H(z), show that whether the system is stable or not.
f) Determine the frequency response of the system, if exists. Why?
g) Determine the impulse response of the inverse system calculated in f).
Transcribed Image Text:The input-output relationship of a discrete-time LTI system is given as follows y[n] = 2x[n – 4] – 3x[n – 6]. a) Determine the impulse response of the system, h[n]. b) Using h[n], show that the system is causal. c) Using h[n], show that whether the system is BIBO stable or not. d) Determine the transfer function H(z). Plot pole-zero diagram. Indicate ROC. e) Using H(z), show that whether the system is stable or not. f) Determine the frequency response of the system, if exists. Why? g) Determine the impulse response of the inverse system calculated in f).
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