EE 643 Project #4 Spring 1999
This project will investigate three methods for FIR filter design ---
windowing, frequency sampling, and the Parks-McClellan algorithm.
Exercises
. Design a filter
using each of the following windows:
Plot the impulse response, magnitude response, and zero-pole locations
of the five filters.
(Use
freqz and
zplane for magnitude
response and pole-zero plots.)
Compare the characteristics of the magnitude response.
= 4, 6, and 9.
Plot the impulse response, magnitude response, and zero-pole locations.
Compare the characteristics of the magnitude response with each other
and with the filters from the first exercise.
How does the trade-off of transition bandwidth and overshoot vary with 
?
. Determine
the desired DFT sample values from the specified cutoff and then take
the inverse FFT
(ifft)
file:/opt/matlab.v5.3/help/techdoc/ref/ifft.html.
Keep in mind that the DFT coefficients must be symmetric to yield a
real impulse response. For example, a cutoff of 
and a
length of 9 would yield a DFT coefficient vector [1 1 1 0 0 0 0 1 1]
corresponding to the frequency values
2*pi*[0 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9].
Plot the impulse response, magnitude response, and zero-pole locations.
Compare the characteristics of the magnitude response to the other
designs.
and a stopband
cutoff of 
.
Plot the impulse response, magnitude response, and zero-pole locations.
Compare the characteristics of the magnitude response to the other
designs.
, a stopband
cutoff of 
, and the largest possible stopband attenuation.
(Use ellipord by trial and error to determine this.) Compare
the magnitude response to the Parks-McClellan filter. Note that a
12th-order IIR filter requires approximately the same number of
multiplies per output point as a 23rd order FIR filter.
auread.
Using the
fft function,
determine the frequencies of the upper and lower tone of the doorbell.
Using trial-and-error,
design a filter using any of the FIR techniques above such that the lower
tone is attenuated no more than 3 dB while the upper tone is attenuated
as much as possible. Describe how you designed your filter.
auwrite
the resulting signal as the file newdoor.au. Email the file to
me as an attachment. The best result gets a gold star and a certificate
suitable for framing. ;-)
Write a short report describing your findings. The report should
contain a concise description of your results.
Include listings of your function. Be sure to answer all questions.
You are not expected to include in
the report all plots which you were required to do; instead, you should
summarize in your report the important features of the unincluded plots.
For further help: