**Prerequisites**:

Background in undergraduate level signal processing, probability and statistics,

e.g., ECE 431 and 331

**Instructor**:

Robert Nowak

E-mail: nowak@engr.wisc.edu

Web: http://www.ece.wisc.edu/~nowak/

Phone: 608 265 3914

3627 Engineering Hall

Office Hours: after lecture, Tuesday and Thursday, 12:15-1:15pm

**Teaching Assistant**:

Kei Hao

E-mail: khao@wisc.edu

Office Hours: Tuesday and Thursday, 2-3pm, B630 Engineering Hall

**Lectures**:

Fall 2003

Tuesday, Thursday 11:00 AM – 12:15 PM

3032 Engineering Hall

**Discussion Sessions**:

The TA will hold a weekly discussion session to review homework problems/solutions,

discuss projects, and review topics covered in the lectures.

Time: Thursdays 5:30-7pm

Place: 3355 Engineering Hall

**Course Notes**: available for purchase at Bob’s Copy Shop

**Textbook**: none

**Grading and Evaluation**:

Two Midterms: 40% (20% each)

Exam 1: handed-out at class Oct 21, due Oct 23

Exam 2: handed-out at class Dec 9, due Dec 11

Three Projects: 45% (15% each)

Homework & Course Participation: 15%

Keeping up with the course and participating in lectures (asking questions)

is very important to successful learning. Keep your homework solutions organized

in a folder or binder. I will ask you to turn in your solutions from time to time

to see how you are keeping up with the coursework.

**Course Outline**:

1. Minimum Mean Square Error Estimation and Filtering

– mean square error

– orthogonality principle

– Wiener filtering

– adaptive filtering and the Least Mean Square algorithm

2. Spectral Estimation: The Basics

– Periodogram

– Non-parametric Spectrum Estimation

– Parametric Methods

– Minimum Variance and Eigenanalysis Methods

3. Time Meets Frequency

– Time-frequency Analysis

– Windowed Fourier Transform

– Wavelet Transforms

– Instantaneous Frequency

– Quadratic Time-Frequency Distributions

4. Wavelet and Multiresolution Signal Analysis

– Signal Spaces

– Signal Bases and Frames

– Wavelet Transforms

5. Filter Banks and the Discrete Wavelet Transform

– Discrete Wavelet Transform

– Analysis and Synthesis Filter Banks

– Regularity and Vanishing moments

– Approximation Theory

6. Wavelet-Based Signal and Image Processing

– Image Compression and Coding

– Denoising

**Reference Textbooks (not required, on reserve at Wendt Library)**:

Oppenheim and Schafer, Discrete Time Signal Processing, Prentice-Hall, 1989.

Haykin, Adaptive Filter Theory, Prentice Hall, 1986.

Solo and Kong, Adaptive Signal Processing Algorithms, Prentice Hall, 1995.

Mallat, A Wavelet Tour of Signal Processing, 2nd edition, Academic Press, 1999

Burrus, Gopinath, and Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, Prentice Hall, New Jersey, 1998

Kay, Modern Spectral Estimation : Theory and Application, Prentice Hall, 1988

Proakis and Manolakis, Digital Signal Processing, 3rd edition, Prentice Hall, 1996

Flandrin, Time-Frequency / Time-Scale Analysis, Academic Press, 1999

**
Useful Websites**:

Rice Wavelet Toolbox for Matlab Computational Mathematics Laboratory

Rice University