Amir-Homayoon Najmi has a BA degree in mathematics from Cambridge University, and a PhD 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 Bellaire Geophysical Research Centre prior to joining the Johns Hopkins University Applied Physics Laboratory. He has published research in wide areas, including quantum field theory in cosmological space-times, seismic inverse scattering, 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 JHU’s Whiting School of Engineering. His book, Wavelets: A Concise Guide was published by the Johns Hopkins University Press in 2012.
This is an introductory course on wavelet analysis, with an emphasis on the fundamental mathematical principles and basic algorithms. We cover the mathematics of signal (function) spaces, orthonormal bases, frames, time-frequency localization, the windowed Fourier transform, the continuous wavelet transform, discrete wavelets, orthogonal and biorthogonal wavelets of compact support, wavelet regularity, and wavelet packets. It is designed as a broad introduction to wavelets for engineers, mathematicians, and physicists.Prerequisite: Competence with multivariable calculus, linear algebra, and a scientific programming language is required, as well as familiarity with Fourier transforms and signal processing fundamentals such as the discrete Fourier transform, convolutions, and correlations.
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.
- Mathematical structures of signal spaces.
- Implementation of the continuous wavelet transform.
- Implementation of the discrete wavelet transform.
- Implementation of Wavelet Packet Transforms and the Best Basis Algorithm.
When This Course is Typically Offered
Fall, every academic year. Dorsey campus.
- 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
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.
Textbook information for this course is available online through the MBS Direct Virtual Bookstore.
There are no notes for this course.
Final Words from the Instructor
"Wavelets: A Concise Guide", A. H. Najmi, Johns Hopkins University Press, 2012.
(Last Modified: 03/19/2012 04:25:47 PM)