How Much Do You Remember About Filter Design (1 Design a simple, discrete-time filter with the following properties IIR, causal, and stable H\left(e^{j \omega}\right)=0 \text { at } \omega=\{0.85 \pi,

0.9 \pi, 0.95 \pi\} H\left(\mathrm{e}^{j \omega}\right) \text { has a resonant peak at } \omega=0.2 \pi The filter should have a notch at 1/9 Use the smallest filter order that meets the requirements. Choose a value for r (and a different value of r for the notch) and determine the gain that is needed to make Write an expression for H(2) and show the pole-zero plot. Roughly sketch what H(e) lookslike.