Question

When the input to an LTI system is x[n] = (1/2)^n u[n] + 2^n u[-n - 1] the output is y[n] = 6 (1/2)^n u[n] - 6 (3/4)^n u[n] (a) Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the ROC. (b) Find the impulse response of the system for all values of n. (c) Write the difference equation that characterizes the system. (d) Is the system stable? Is it causal?

          When the input to an LTI system is
x[n] = (1/2)^n u[n] + 2^n u[-n - 1]
the output is
y[n] = 6 (1/2)^n u[n] - 6 (3/4)^n u[n]
(a) Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the ROC.
(b) Find the impulse response of the system for all values of n.
(c) Write the difference equation that characterizes the system.
(d) Is the system stable? Is it causal?

When the input to an LTI system is
x[n] = (1/2)^n u[n] + 2^n u[-n - 1]
the output is
y[n] = 6 (1/2)^n u[n] - 6 (3/4)^n u[n]
(a) Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the ROC.
(b) Find the impulse response of the system for all values of n.
(c) Write the difference equation that characterizes the system.
(d) Is the system stable? Is it causal?

Added by Mar-A B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sri K

02/27/2023

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When the input to an LTI system is x[n] = (1/2)^n u[n] + 2^n u[-n-1], the output is y[n] = 6(1/2)^n u[n] - 6(3/4)^n u[n]. (a) Find the system function H(z) of the system. Plot the poles and zeros of H(z), and indicate the ROC. (b) Find the impulse response of the system for all values of n. (c) Write the difference equation that characterizes the system. (d) Is the system stable? Is it causal?