2) Suppose we want to design a discrete-time LTI system which has the property that if the input is п-1 x[n] = ()" u[n] -;G" un – 1). Then the output is y[n] = u[n]. a) Find the impulse response and frequency response of a discrete-time LTI system that has the foregoing property. b) Find a difference equation relating x[n] and y[n] that characterizes the system. c) Suppose that a system has the response () u[n] to the input (n + 2) (;) u[n]. If the output of this system is 8[n] - (-)" u[n], what is the input?

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2) Suppose we want to design a discrete-time LTI system which has the property that if the input is
п-1
x[n] = ()" u[n] -;G)" un – 1).
Then the output is
y[n] = ) u[n].
a) Find the impulse response and frequency response of a discrete-time LTI system that has the
foregoing property.
b) Find a difference equation relating x[n] and y[n] that characterizes the system.
c) Suppose that a system has the response (-) u[n] to the input (n + 2) ) u[n]. If the output
of this system is 8[n] - (-)" u[n], what is the input?
Transcribed Image Text:2) Suppose we want to design a discrete-time LTI system which has the property that if the input is п-1 x[n] = ()" u[n] -;G)" un – 1). Then the output is y[n] = ) u[n]. a) Find the impulse response and frequency response of a discrete-time LTI system that has the foregoing property. b) Find a difference equation relating x[n] and y[n] that characterizes the system. c) Suppose that a system has the response (-) u[n] to the input (n + 2) ) u[n]. If the output of this system is 8[n] - (-)" u[n], what is the input?
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