## EE 451

**Homework Assignment 11 **

Due Nov. 8, 2000

- 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.
- 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

- 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 >
*