Purdue University
School of Electrical and Computer Engineering
EE648 Wavelet, Time-Frequency, and Multirate Signal Processing
Spring 2003
Prof. Ilya Pollak
Note: Many documents on this website are in Acrobat format. To download
a free version of the Acrobat viewer, go to
the Adobe web site.
Course TA: Yan Huang, MSEE 176, 494-3465, yanh@ecn.purdue.edu.
Office hours: Thursdays 2-3pm.
Other strongly recommended books:
G. Strang, T. Nguyen. "Wavelets and Filter Banks".
Wellesley-Cambridge Press, 1997. ISBN 0-9614088-7-1
I. Daubechies. "Ten Lectures on Wavelets".
Philadelphia: Society for Industrial and Applied Mathematics, 1992.
ISBN 0-89871-274-2
M. Vetterli, J. Kovacevic. "Wavelets and Subband Coding." Prentice Hall, 1995.
ISBN 0-13-097080-8
The main theme of this course is sparse representations of
signals. Orthogonal bases are of particular
interest because they can efficiently approximate certain
types of signals with just a few vectors. Two examples
of such applications which will be studied in this course
are image compression and estimation of noisy signals.
We will consider several approximation schemes. For example,
a linear approximation projects the signal over M vectors
chosen a priori. Better approximations are obtained by
choosing the M basis vectors adaptively, depending
on the signal. A further degree of freedom is introduced by
choosing the basis itself adaptively, from a family of bases.
In this context, a number of very successful recent algorithms
for nonlinear approximation, noise removal, and feature extraction
will be considered, such as wavelet thresholding, best basis
search, and matching pursuit.
Several types of orthogonal bases will be studied: wavelet
bases, wavelet packet bases, and local cosine bases. We will
study their properties, as well as fast algorithms for calculating
the coefficients of a signal with respect to a basis and for
reconstructing the signal from its coefficients. We will also
address time-frequency properties of various signal
decompositions--which is an important tool in deciding what
decomposition is appropriate for a particular application.
The pre-requisite for this course is thorough understanding
of fundamentals of signal processing--such as Fourier analysis
and sampling. These topics will be reviewed at the beginning
of the course.
The administration of the course will be very simple: the final
grade will be determined solely on the basis of four problem sets
which you can think of as take-home exams. Tentative
due dates for the problem sets are: February 17, March 10, April 14,
April 28. Each problem set will be posted on the course web site
approximately one month before its due date. Each problem set is
due in class for on-campus students and must be postmarked by
the due date for off-campus students.
No collaboration with anyone is allowed
on the problem sets; however, you can use any literature you wish.
There will be no in-class exams and no final.