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ECE 425
Digital Signal Processing
Fall 2009
Phase and the DTFT
This is a 2-week lab (weeks of September 14 and 24).
Write-ups are due by 4pm on Friday, October 2 in the 425 lock-box.
The DSP lab is 303 Phillips.
Note that the lab has “TA checks” throughout. You must demonstrate the indicated
requirement to your lab TA, who may then ask you follow-up questions or point out particular
features of interest. Completing the TA checks is a crucial part of the laboratory. If you simply turn
in the questions, you will fail the laboratory component of this course.
Prelab
1.
Read the entire lab, especially the “Helpful Hints” section at the end.
2.
Read the questions at the end.
3.
The course web page provides two Matlab tutorials. Read one or both (they are very fast
and easy reading) prior to your lab session.
Introduction
This lab provides several experiments involving phase — that part of the DTFT that we rarely
talk about. In fact, phase is very important — a filter which has a “nice” phase behavior but non-
flat magnitude behavior may sometimes be more desirable than one with “nice” magnitude
behavior but uncooperative phase behavior. (We will discuss in class an example in which “nice”
phase behavior is particularly important — modelling the human visual system’s response to
temporal artifacts in highly distorted video sequences coded for extremely low-rate transmission,
e.g. to a cell-phone or a fast-moving receiver.) After you do the lab, you will understand “nice”
and “uncooperative” in a more quantitative sense.
Frequency Responses
In the first part of the lab, you’ll compare frequency responses for three related filters. First,
define a low-pass filter h with the following coefficients:
h = [ -0.06453888262894
-0.04068941760956
0.41809227322221
0.78848561640566
0.41809227322221
-0.04068941760956
-0.06453888262894];
h = h/sum(h);
(You don’t need to type them in to this many significant digits! Three will do just fine.) Dividing
by
sum(h)
normalizes the filter’s DC response to 1. (This is the 7-tap low-pass wavelet filter

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from the bi-orthogonal wavelet filters known as “Daubechies seven-nine filters.” These filters are
used extensively in image/video processing and compression.)
Use the
freqz
command (read the help!) to compute the frequency response
at 512
points between 0 and
. Have it return the frequencies themselves as well, since you’ll be using
them later:
[H, W] = freqz(h, 1);
Plot the magnitude and phase of the frequency response (on separate graphs):
figure(1);
plot(W, abs(H));
figure(2);
plot(W, angle(H));
*TA check
— magnitude and phase plots for the given filter.
You should observe obvious low-pass behavior in the magnitude response. You should also
observe linear-phase behavior: the phase response is a straight line (Matlab wraps it around so the
returned angle is always less than
in absolute value). The “straight line” may be easier to see if
you unwrap the phase:
plot(W, unwrap(angle(H)));
Now consider 2 more filters:
, and
. Compute and
compare the magnitude and phase responses of these filters with those of
.

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