Question: Problem I. A discrete - time LTI system is specified by the difference equation y [ k + 1 ] 0 . 5 y [

Problem I.
A discrete-time LTI system is specified by the difference equation
y[k+1]0.5 y[k]=[k+1]+0.8[k].
a) Derive its transfer function in the z-domain.
b) Find the amplitude and phase response of the system.
c) Find the system response y[k] for the input [k]= cos(0.5k 37).

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