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                              COURSE ANNOUNCEMENT
                                    FALL 1997
                                    EECS 551
                        DETERMINISTIC SIGNAL PROCESSING
            (EMPHASIS ON WAVELETS AND TIME-FREQUENCY DISTRIBUTIONS)
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This course introduces concepts in transforms and applications in Fourier
time-frequency localization.  Wavelet transforms and series, filter banks, fast
algorithms and applications.  Time-frequency distributions including Wigner,
Cohen class, Choi-Williams and applications.  

WHO SHOULD TAKE THIS COURSE: Wavelets and time-frequency distributions are
presently very active areas of both research and applications.  Most signal
processing majors should take it.  Graduate students in other areas such as
electromagnetics who are interested in wavelets for Green's function sparse
representations, should also consider this course (EECS 451 (DSP) is VITAL).

LECTURES: Tuesday & Thursday, 10:00-11:30 AM, 1003 EECS 
INSTRUCTOR: Professor Andrew E. Yagle, 4114 EECS, 763-9810, aey@eecs.umich.edu
GRADING: 2 exams and 1 final @30% each.  Weekly problem sets @10% total.
WEB PAGE: http://www.eecs.umich.edu/~aey

PREREQUISITE: EECS 451 or equivalent, or permission of the instructor.
WAVELETS TEXT: M. Vetterli and J. Kovacevic, "Wavelets and Subband Coding."
COURSE NOTES (distributed in class) will also be used. 
CLOSED  I. Daubechies, 10 Lectures on Wavelets
RESERVE C.K. Chui, Wavelets: Tutorial in Theory and Applications
TEXTS:  A.K. Akansu and R. Haddad, Multiresolution Signal Decomposition

WEEK                               TOPICS
1 Review of DTFT and digital filtering
2 Decimation and interpolation.  Multirate signal processing 
3 Orthonormal signal representations, including Fourier.  Hilbert spaces.
4 Filter banks: orthogonal, quadrature-mirror, octaves.
5 Wavelet representation of signals: multiresolution analysis, orthogonalization
  Examples: Haar, sinc (constant Q), spline (leads to Battle-Lemarie).
6 Wavelet basis construction using Fourier methods and iterated filter banks:

  scaling function:  pulse   B-spline   sinc       softsinc   Daubechies
  wavelet function:  Haar    Battle-    Paley-     Meyer      Daubechies
                             Lemarie    Littlewood

7 Wavelet series, t-f sampling, Morlet wavelet, properties.  2-D wavelets.
8 Fast wavelet alg. (Mallat), mult voices. APPLICATION: Operator sparsification.
9 APPLICATIONS: compression, subband coding, image coding, local filtering.
10 T-F plane: uncertainty principle, frames, STFT, DSTFT, spectrogram.
11 TFD properties (marginals, chirps etc.) Wigner-Ville. Kernels, Cohen's class.
12 Cross terms, Choi-Williams, ambiguity func, local autocorrelation. Relations.
13 APPLICATIONS: analysis of nonstationary biological and mechanical signals.
14 Review, course evaluations

NOTE: In previous incarnations this course concentrated on Hilbert space signal
representation.  In the present incarnation the course will specialize this to
wavelet and time-frequency signal representations, and also introduce digital
signal processing concepts (multirate filtering and orthogonal filter banks).

For more information please contact the instructor (email is best).