Question

6 Filter Design (10 pts) Design a simple, discrete-time filter with the following properties • IIR, causal, and stable Н(ei) %3D0 at w 3 {0.5л, 0.75т} H(e") has a resonant peak at w = 0.25# • Two free parameters (C and r) for controlling the amplitude and the sharpness (qualityfactor) of the resonant peaks (same parameters control both peaks). • Use the smallest filter order that meets the requirements. Choose a value for r anddetermine the gain that is needed to make H(ej0)= 1 Write anexpression for H(z) and show the pole-zero plot.

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