Course Details
Subject {L-T-P / C} : MA5148 : Wavelet Analysis { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Divya Singh
Syllabus
Review of Fourier series, Fourier transform on L1 (R) and L2 (R), basic properties and examples Windowed Fourier Transform, Orthonormal basis generated by a single function, Balian-Low theorem, The Gabor transform, Wavelet Transform, Dyadic wavelets and examples, Spline wavelets, Daubechies wavelets, Multiresolution Analysis and construction of orthonormal wavelets, Properties of scaling functions, Some applications of wavelets.
Course Objectives
- To identify the limitations of classical Fourier analysis
- To introduce the construction of wavelets with some specific examples
Course Outcomes
Students will learn about the characterization of wavelets in L2(R) and the most powerful technique MRA (Multiresolution Analysis) for the construction of wavelets. Daubechies wavelets are constructed through MRA. Also they will learn about Spline wavelets and some of its applications in signal/image processing.
Essential Reading
- E. Hernandeze and G. Weiss, A first course on wavelets, CRC Press
- D. F. Walnut, An introduction to wavelet analysis, Birkhäuser
Supplementary Reading
- G. Bachman, L. Narici, and E. Beckensterin, Fourier and Wavelet Analysis, Springer-Verlag
- C.K . Chui, An Introduction to Wavelets, Academic Press