525.762 - Signal Processing with Wavelets Course Homepage
Instructor Information
Amir-Homayoon Najmi
Email: najmi@jhuapl.eduWork Phone: 443.778.3320
Dr. Najmi has a B.A. degree in Mathematics from Cambridge University, and a D.Phil. in Theoretical Physics from Oxford University. He was a Fulbright scholar at the Relativity Centre, University of Texas, a Research Associate and Instructor at the University of Utah and a Research Physicist at Shell Oil Geophysical Research centre prior to joining the Johns Hopkins University APL. He has published research in wide areas including quantum field theory in cosmological space-times, seismic inverse scattering, and adaptive signal processing applied to electromagnetic waves and biosurveillance. He has developed and taught courses in Relativity, Astrophysics, Cosmology, Advanced Signal Processing and Wavelet Signal Analysis at the Whiting school, and he is an adjunct associate professor at UMBC where he has taught a course in General Relativity.
Course Information
Course Description
This course presents the fundamentals of wavelets as a signal processing tool. Topics include continuous and discrete-time wavelets, time-frequency transient analysis, wavelet bases, wavelet packets, and approximations with wavelets. Applications include signal and image denoising (filtering), and compression. Computer experiments using Matlab illustrate the techniques studied.
Prerequisites
525.427, Digital Signal Processing and the basics of linear systems.
Course Goal
A thorough understanding of the mathematical basis of the wavelet transform as a tool in signal and image analysis and applications to time-frequency analysis, signal denoising and image compression.
Course Objectives
- Mathematical structures of signal spaces.
- Implementation of the continuous wavelet transform.
- Implementation of the discrete wavelet transform.
When This Course is Typically Offered
Fall, every academic year. Dorsey campus.
Syllabus
Topics Covered
- Linear algebra, Hilbert spaces, Frames
- Fourier transforms
- Time and Frequency analysis
- Haar wavelet
- Shannon wavelet
- Multi resolution analysis
- DWT of discrete time signals
- orthogonal wavelet packets
- wavelet regularity and Daubechies construction
- wavelet transform of images
Student Assessment Criteria
| Homework | 30% |
| Implementation projects | 70% |
Computer and Technical Requirements
Working familiarity with a computer language that can handle data plotting and images is required. Examples: IDL, Matlab. Any other programming language (Fortran, C, etc) that can plot signals and display images.
Familiarity with discrete signals and linear algebra is assumed, although both will be reviewed.
Textbooks
Textbook information for this course is available online through the MBS Direct Virtual Bookstore.
Course Notes
There are notes for this course.
(Last Modified: 08-20-2009 at 1:39:46 PM)