EC846 Wavelet Transforms
Announcements
- Test 2 Solution
- Test1+Event2+Test2 Marks
- Event 4 Deadline April 18 2018
- Event 2 Deadline March 10 2018
- Test1 Question Paper Solution Marks
- Dr.SPK's book first two chapters(Revised 14 March 2017)
History: Where do wavelets come from? An Article by Ingrid Daubechies
Lifting Wavelets; Tutorial by Daubechies & Sweldens
original paper by Sweldens
Talk given by Dr. S. P. K. at CNC 2012 Chennai
Syllabus Outline
Unit 1: Linear Algebra Review: Vector spaces and basis, inner products, diagonalization, shift invariant linear transform, convolution and DFT, signal as vector representation using Fourier basis, Concept of Approximation and error vector.
Unit 2: Construction of discrete wavelets: Mother wavelets and scaling function, first stage wavelet basis, iteration, Multi resolution analysis, Filter bank, Up-sampling, Down sampling, Quadrature mirror filters and conjugate filters, Haar transform as rotation operator, Daubechies orthogonal wavelets, Shannon wavelet
Unit 3: Construction of continuous wavelets (in time domain and frequency domain), Filter implementation, wavelets with compact support, Examples: beta wavelet, Mexican hat wavelet, Shannon wavelet, Daubechies Wavelets and Vanishing Moments.
Biorthogonal wavelets: Mathematical Condition on Filters, Examples Bior 1.3, Bior 2.5
Unit 4: Applications: Image compression, feature extraction, edge detection, audio masking, denoising
Unit 5: Lifting wavelet scheme: Polyphase representation, Laurent polynomials, Lifting properties and applications.
Books:
- Michael Frazier, An Introduction to Wavelets through Linear Algebra, Springer Edition. (For good foundation and excellent mathematical perspective).
- Raghuveer M. Rao, Ajit Bopardikar, Wavelet Transforms: Introduction to Theory and Applications, Pearson Publication. (For good engineering perspective).
- K. P. Soman, K I Ramachandran, N G Resmi, Insight into Wavelets: From Theory to Practice, PHI Eastern Economy Edition