EC846 Wavelet Transforms

Announcements

1. Test 2 Solution
2. Test1+Event2+Test2 Marks
3. Event 4 Deadline April 18 2018
4. Event 2 Deadline March 10 2018
5. Test1 Question Paper Solution Marks
6. 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:

1. Michael Frazier, An Introduction to Wavelets through Linear Algebra, Springer Edition. (For good foundation and excellent mathematical perspective).
2. Raghuveer M. Rao, Ajit Bopardikar, Wavelet Transforms: Introduction to Theory and Applications, Pearson Publication. (For good engineering perspective).
3. K. P. Soman, K I Ramachandran, N G Resmi, Insight into Wavelets: From Theory to Practice, PHI Eastern Economy Edition