Problem 2 Let's use an intuitive, graphical approach to design a simple, discrete-time filter with the following properties • IIR, causal, and stable -H\left(\mathrm{e}^{j \omega}\right)=0 \text { at } \omega=\{0,

.4 \pi, \pi\} H\left(\mathrm{e}^{\mathrm{j\omega}}\right) \text { has a resonant peak at } \omega=\{.2 \pi, .8 \pi\} Two free parameters for controlling the amplitude and the sharpness (quality factor) of the resonant peaks (same parameters control both peaks); leave these two parameters as constants that the user may choose. Use the smallest filter order that meets the requirements. Show the pole-zero diagram, a plot of the magnitude and phase response of the DTFT,and write out the transfer function H(z).

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