AMCS 237: Fourier and Wavelet Theory (Fall 2023)
The course provides a detailed and mathematically precise introduction to Fourier, Wavelet and multiresolution analysis from a computational point of view. This includes algorithmical aspects, complexity analysis, and exemplary applications relevant to scientific and visual computing.
Goals and Objectives
The course is algorithmically oriented aiming to enable the students to develop principled computational methods for problems related to Fourier, Wavelet and multiresolution analysis.
The course will assume solid knowledge (calculus and linear algebra) such as taught in undergraduate mathematics courses or in AMCS 101, 131, and 151.
Assignments and Evaluation
There will be a problem set assigned each week to prepare for the final exam. This homework track is mostly theoretical, but it will include smaller programming tasks along the way. The students may collaborate on the assignments. Grading policy: 100% final exam.
Function Spaces and Fourier Series
Continuous-time Fourier Transform (CTFT)
Laplace Transform and Bromwich Integral
Discrete-time Fourier Transform (DTFT)
Fast Fourier Transform (FFT) and the Cooley-Tukey FFT Algorithm
Rader's FFT Algorithm
Chirp Z-transform (CZT) and Bluestein's Algorithm
Windowed Fourier Transform (WFT) and Heisenberg’s Uncertainty Principle
Discrete Cosine Transform (DCT)
Continuous-time Wavelet Transform (CTWT)
Discrete-time Wavelet Transform (DTWT)
Mallat's Multiresolution Analysis (MRA)
Fast Wavelet Transform (FWT)
J. C. Goswami and A. K. Chan
Fundamentals of Wavelets: Theory, Algorithms, and Applications
A Friendly Guide to Wavelets
K. P. Ramachandran, K. I. Resmi, and N. G. Soman
Insight into Wavelets: From Theory to Practice
D. K. Ruch and P. J. Van Fleet
Wavelet Theory: An Elementary Approach with Applications
E. J. Stollnitz, A. D. DeRose, and D. H. Salesin
Wavelets for Computer Graphics: Theory and Applications
Morgan Kaufmann, 1996
Prof. Dr. Dominik L. Michels
Dr. Dmitry A. Lyakhov
8:30 AM – 10:00 AM | Sun Wed | 2023-08-27 – 2023-12-06 | Bldg 1, R 2107