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18.327/1.130: Wavelets, Filter Banks and Applications Problem Set 1

This document provides the details of Problem Set 1 for the course 18.327/1.130: Wavelets, Filter Banks and Applications. It includes two Matlab exercises to analyze different filter banks and signals. It also lists four textbook problems from different chapters to complete for the problem set. Students are to submit their Matlab code and plots by the due date of SES #6.

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40 views1 page

18.327/1.130: Wavelets, Filter Banks and Applications Problem Set 1

This document provides the details of Problem Set 1 for the course 18.327/1.130: Wavelets, Filter Banks and Applications. It includes two Matlab exercises to analyze different filter banks and signals. It also lists four textbook problems from different chapters to complete for the problem set. Students are to submit their Matlab code and plots by the due date of SES #6.

Uploaded by

MelbinGeorge
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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18.327/1.

130: Wavelets, Filter Banks and Applications


Problem Set 1

Issued: SES #3 Due: SES #6

Matlab Exercises
Please submit your Matlab code and plots.
1. Consider a two channel
√ √perfect reconstruction
√ filter√bank (see pp. 103 in the text) with the analysis fil­
ters h0 [n] = {1/ 2, 1/ 2} and h1 [n] = {1/ 2, −1/ 2}. Consider also a signal x[n] = {0, 1, −1, 2, 5, 1, 7, 0}.
(a) Find the corresponding dual(synthesis) filters f0 [n] and f1 [n].
(b) Find (and plot) the signals v0 [n], v1 [n] and x[n].
(c) Plot the zeros of the filters h0 [n], h1 [n], f0 [n] and f1 [n] (use zplane).
(d) Plot the frequency spectra of v0 [n] and v1 [n].
√ √
2. Repeat the previous problem for the filters h0 [n] = {−1, 2, 6, 2, −1}/(4 2)} and h1 [n] = {1, −2, 1}/(2 2).

Textbook Problems
1. Problem Set 1.3, pp. 15. Problems 1 and 3.
2. Problem Set 1.4, pp. 21. Problems 9 and 11.
3. Problem Set 3.3, pp. 100. Problems 2 and 7.
4. Problem Set 4.1, pp. 113–114. Problems 3, 4, 9 and 12.

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