3.16. When the input to an LTI system is -()" i) u[n] + (2)"u[-n – 1), x[n] = the corresponding output is y[n] = 5 () uln] – 5 () uln). (a) Find the system function H(z) of the system. Plot the pole(s) and zero(s) of H (2) and indicate the ROC. (b) Find the impulse response hin] of the system. (c) Write a difference equation that is satisfied by the given input and output. (d) Is the system stable? Is it causal?

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3.16. When the input to an LTI system is
x[n] =
u[n] + (2)" u[-n – 1),
%3D
the corresponding output is
y{n] = 5() uln] –- 5
) u[n).
(a) Find the system function H(z) of the system. Plot the pole(s) and zero(s) of H (z) and
indicate the ROC.
(b) Find the impulse response h[n] of the system.
(c) Write a difference equation that is satisfied by the given input and output.
(d) Is the system stable? Is it causal?
Transcribed Image Text:3.16. When the input to an LTI system is x[n] = u[n] + (2)" u[-n – 1), %3D the corresponding output is y{n] = 5() uln] –- 5 ) u[n). (a) Find the system function H(z) of the system. Plot the pole(s) and zero(s) of H (z) and indicate the ROC. (b) Find the impulse response h[n] of the system. (c) Write a difference equation that is satisfied by the given input and output. (d) Is the system stable? Is it causal?
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