When the input to a linear time-invariant system is x[n] = (1/2) n u[n] + (2) n
Question:
When the input to a linear time-invariant 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 region of convergence.
(b) Find the impulse response h[n] 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?
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Related Book For 
Discrete Time Signal Processing
ISBN: 978-0137549207
2nd Edition
Authors: Alan V. Oppenheim, Rolan W. Schafer
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