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Course Objective
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To provide a
solid theoretic background of multirate filter
banks and wavelet, you should master the
principles and design methods of some types of
filter banks, and applications in related
fields, such as communications, signal
processing and image processing, etc. The
ultimate aim of this course is expected to
benefit to your own applications fields of
interest.
Upon completion
of the course, you should be able to:
• Be
familiar with techniques for designing filter
bank.
•
Understand the terminologies that are used in
the wavelets literature.
•
Understand the concepts and theory behind
wavelets constructions from an
interdisciplinary perspective that unifies
harmonic analysis (mathematics), filter banks
(signal processing), and multiresolution
analysis (computer vision).
• Be
familiar with the modern signal processing using
signal spaces, bases, operators
and series expansions.
• Apply
wavelets and multiresolution techniques to a
problem at hand, and justify why
wavelets provide the right tool.
•
Research, present, and report a selected project
within a specified time.
• Think
critically, ask questions, and apply problem
solving techniques. |
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Lecturer
Prof.
Guangming Shi,
Research
Assistant Pro. Alfonso Fernandez-Vazquez ,
Associate Prof. Xuemei Xie.
Address:
A102, A710 New Technology and Research Building
Phone:
86+29+88201020, 88204453
E-mail:
gmshi@xidian.edu.cn
xmxie@mail.xidian.edu.cn
Lectures
Tuesday: 8:30 ¨C 10:10,
J3-08 .
Friday:
8:30 ¨C 10:10, J3-08(single number of week).
Course Homepage
http://www.hetaojiu.org/faculty/gmshi/
Prerequisites
Digital Signal
Processing; Matlab; Linear Algebra.
Level
Postgraduate
students in the fields of
communication, signal
processing, circuit and system
and intelligent
information processing, etc.
Topics
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|
NO. |
DATE |
TITLE |
|
1 |
6th
Mar. |
Introduction and filter design techniques |
|
2 |
9th
Mar. |
Multirate system fundamentals |
|
3 |
13th
Mar. |
Multirate filter design techniques: IFIR and FM
approach |
|
4 |
20th
Mar. |
Homework explanation |
|
5 |
23rd
Mar. |
Design of two-channel linear-phase/low-delay
filter banks |
|
6 |
27th
Mar. |
Two band filter banks with FIR and IIR filters |
|
7 |
3rd
Apr. |
M-channel
maximally decimated filter banks |
|
8 |
6th
Apr. |
M-channel
near-perfect-reconstruction cosine-modulated
filter banks |
|
9 |
10th
Apr. |
M-channel
perfect reconstruction cosine modulated filter
banks |
|
10 |
17th
Apr. |
Assignment explanation and paper intepretation |
|
11 |
20th
Apr. |
Non-uniform filter banks |
|
12 |
24th
Apr. |
M-channel
linear phase filter banks |
|
13 |
8th
May |
Homework explanation |
|
14 |
15th
May |
Multiresolution analaysis and wavelet theory |
|
15 |
18th
May |
Comparison of wavelet and Fourier transform |
|
16 |
22nd
May |
Filter banks and discrete wavelet transform |
|
17 |
29th
May |
Wavelet with FIR and IIR filters I |
|
18 |
1st
Jun. |
Wavelet with FIR and IIR filters II |
|
19 |
5th
Jun. |
M-band
wavelet |
|
20 |
12th
Jun. |
Wavelet design based on cosine modulated filter
banks |
|
21 |
15th
Jun. |
Wavelet transform application: denoising and
compression |
|
22 |
19th
Jun. |
Matching wavelet |
|
23 |
26th
Jun. |
Homework explanation |
|
6th
Jul. |
Final Report |
¡¡ |
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Textbooks
¡¤
P. P.
Vaidyanathan, Multirate Systems and Filter Banks.
Prentice-Hall. Englewood Cliffs, NJ: 1993.
¡¤
G. Strang
and T. Q. Nguyen, Wavelets and Filter Banks.
Wellesley-Cambridge Press, Wellesley, MA, Revised
Edition, 1998.
¡¤
Stephane
Mallat, A Wavlet Tour of Signal Processing. San
Diego: Academic Press, 1999.
¡¤ M.
Vetterli and J. Kovacevic, Wavelets and Subband Coding,
Prentice Hall, Englewood Cliffs, NJ, 1995.
¡¤
Fusheng Yang, Engineering Analysis and Applications of
Wavelet Transform. Science Press£¬BJ:1999.
Additional Resources
(download)
¡¤
P. P.
Vaidyanathan, ¡°Multirate digital filters, filter banks,
polyphase networks, andapplications: a tutorial¡±,
Proc. IEEE, vol. 78, no. 1, pp. 56-93, January 1990.
¡¤
P. P.
Vaidyanathan, "Theory and design of M-channel
maximally decimated quadrature mirror filters with
arbitrary M, having the prefect reconstructions
property," IEEE Trans. Acoust., Speech, Signal
Processing, vol. 35, no. 4, pp. 476-492, April 1987.
¡¤ R. D.
Koilpillai and P. P. Vaidyanathan, "Cosine-Modulated FIR
Filter Banks Satisfying Perfect Reconstruction," IEEE
Trans. Signal Processing, vol. 40, no. 4, April
1992.
¡¤ T. Q.
Nguyen, "Near Perfect Reconstruction Pseudo-QMF
Banks," IEEE Trans. Signal Processing, vol. 42,
no. 1, pp. 65-76, January 1994.
¡¤
T. Q.
Nguyen, "A tutorial on Filter Banks and Wavelets," In
Proc. IEEE International Conference on Digital Signal
Processing, Cypress, June 1995.
¡¤ Y. P. Lin
and P. P. Vaidyanathan, "Linear Phase Cosine Modulated
Maximally Decimated Filter Banks with Perfect
Reconstruction," IEEE Trans. Signal Processing,
vol. 42, no. 11, November 1995.
¡¤ M. Vetterli
and D. L. Gall, "Perfect Reconstruction FIR Filter
Banks: Some Properties and Factorizations," IEEE
Trans. Acoust., Speech, Signal Processing, vol. 37,
no. 7, pp. 1057-1071, July 1989.
¡¤ M.
Vetterli, "A Theory of Multirate Filter Banks," IEEE
Trans. Acoust., Speech, Signal Processing, vol.
ASSP-35, no. 3, pp. 356-372, March 1987.
¡¤ M. Vetterli
and C. Herley, "Wavelets and Filter Banks: Theory and
Design," IEEE Trans. Signal Processing, vol. 40,
no. 9, pp. 2207-2232, September 1987.
More papers can be found in
http://ieeexplore.ieee.org/Xplore/dynhome.jsp.
Grades
-
Homework: 40%
-
Final Report:
50%
-
Seminar:
10%
Homework
¡¤
The homework is required to be printed and handed in to
Liang Lili (Address: New S&T Building A205-4) on time.
Final
Report
¡¤
Students
are suggested to select one topic to finish. The topics
can be chosen from a list of suggestions provided by the
instructors.
Requirements
¡¤
On homework
and projects, you are permitted to discuss the problems
for clarification purposes, and to help each other with
specific points. However, the overall solution and
write-up should be your own work.
¡¤
All the
format, figures, formulas must be in accordance with the
given template.
¡¤
All the
homework and final report can be written in Chinese or
English.
¡¤
All the homework and
report are accepted with the printed version.
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