Consider a filter with system function (a) Sketch the pole-zero pattern. (b) U...

Consider a filter with system function

(a) Sketch the pole-zero pattern.

(b) Using geometric arguments, show that for the system is a notch filter and provide a rough sketch of its magnitude response if

(c) For choose so that the maximum value of

(d) Draw a direct form II realization of the system.

(e) Determine the approximate 3-dB bandwidth of the system.