lab1.425.09 - ECE 425 Digital Signal Processing Fall 2009...

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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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2 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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This note was uploaded on 01/16/2010 for the course ECE 4250 at Cornell.

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lab1.425.09 - ECE 425 Digital Signal Processing Fall 2009...

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