9.54

What type of window(s) may be used to design a low-pass filter with a passband cutoff frequency ? _p = 0.35 ?, a transition width ? ? = 0.025 ?, and a maximum stopband deviation of ? _s = 0.003?

9.55

Use the window design method to design a minimum-order low-pass filter with a passband cutoff frequency ? _s = 0.45 ?, a stopband cutoff frequency ? _s = 0.5 ?, and a maximum stopband deviation ? _s = 0.005.

9.56

We would like to design a bandstop filter to satisfy the following specifications:

1. What weighting function W( e ^{j ?}) should be used to design this filter?

2. What are the minimum and maximum numbers of extremal frequencies that a type I filter of order N = 128 must have?

9.57

Suppose that we would like to design a low-pass filter of order N = 128 with a passband cutoff frequency ? _p = 0.48 ? and a stopband cutoff frequency of ? _s = 0.52 ?.

1. Find the approximate passband and stopband ripple if we were to use a Kaiser window design.

2. If an equiripple filter were designed so that it had a passband ripple equal to that of the Kaiser window design found in part ( a), how small would the stopband ripple be?

9.58

We would like to design an equiripple low-pass...