******************************************************************************* COURSE ANNOUNCEMENT FALL 1997 EECS 551 DETERMINISTIC SIGNAL PROCESSING (EMPHASIS ON WAVELETS AND TIME-FREQUENCY DISTRIBUTIONS) ******************************************************************************* 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).