Problem 1 We want to design a causal discrete-time LTI system with the property that if the input is æ[n] = (})" u[n] – }G)"-"u[n-1] | then the output is y[n] = (})" u[n]. (a) Determine the impulse response hn] of a system that satisfies the foregoing conditions. (b) Find the difference equation that characterizes this system. (c) Determine a realization of the system that requires the minimum amount of memory. (d) Determine if the system is stable.

Introductory Circuit Analysis (13th Edition)
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EE306 HW7
Problem 1
We want to design a causal discrete-time LTI system with the property that if the input is
a|n] = ()" u[n] – 4(G)"-un-1]
then the output is
y[n] = (})" u[n].
(a) Determine the impulse response h[n] of a system that satisfies the foregoing conditions.
(b) Find the difference equation that characterizes this system.
(c) Determine a realization of the system that requires the minimum amount of memory.
(d) Determine if the system is stable.
Transcribed Image Text:1),pdf 1 / 2 100% fig.pdf EE306 HW7 Problem 1 We want to design a causal discrete-time LTI system with the property that if the input is a|n] = ()" u[n] – 4(G)"-un-1] then the output is y[n] = (})" u[n]. (a) Determine the impulse response h[n] of a system that satisfies the foregoing conditions. (b) Find the difference equation that characterizes this system. (c) Determine a realization of the system that requires the minimum amount of memory. (d) Determine if the system is stable.
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