## EE 451

Homework Assignment 11
Due Nov. 8, 2000

1. Problem 8.15. Also, complete the design of the three filters. Do all the Butterworth design by hand. (You can use MATLAB to do the arithmetic, similar to the sheet handed out in class, but you should design the continuous time filter, find the poles and zeros, and transform those to the discrete time filter.) Do the Chebyshev (either Type I or Type II) and elliptic filters using the MATLAB canned routines. For all filters, plot the pole-zeor diagrams and gain. Show that the filters meet the specifications.

2. Repeat Problem 1 for a high-pass filter with the following specifications:
• Passband Ripple: <= 0.2 dB
• Passband Edge: 8 kHz
• Stopband attenuation: >= 30 dB
• Stopband Edge: 4 kHz
• Sampling Rate: 48 kHz

3. Design a Butterworth IIR bandpass filter with the following specifications:
• Passband Ripple: <= 1 dB
• Passband Range: 8 kHz < |F| < 12 kHz
• Stopband attenuation: >= 30 dB
• Stopband Ranges: |F| < 2 kHz and |F| > 16 kHz
• Sampling Rate: 48 kHz
You should find the specifications of the DT filter, transform those into the specifications a CT low-pass filter, design (i.e., find poles and zeros) of a CT Butterworth filter to meet the specifications, then transform the CT low-pass filter to a DT band-pass filter. Plot the poles and zeros, gain and phase of the DT band-pass filter. You can check your work using the MATLAB buttord() and functions.

Bill Rison, <rison@ee.nmt.edu >