### MA6003 Theory of Wavelets (modified)

#### Course Details

Unit 1: A quick review of Fourier series in L^{2}(T) and Fourier transform on L^{2}(R), Genesis of Wavelets, Short time Fourier transform, Properties and Orthogonality relation, Inversion formula Continuous wavelet transform, Orthogonality relation and Inversion formula (13 lectures)

Unit 2: Discretization, Frames and Riesz bases, Frame operators, Gabor frames and Wavelet frames, Balian-Low theorem (12 lectures)

Unit 3: Multiresolution analysis, System of translates, Construction of wavelets from Multiresolution analysis, Daubechies compactly supported wavelets, Some well known examples of wavelets (15 lectures)

#### Course References:

Text Books:

1. O. Christensen, Frames and Bases : An Introductory Course, Springer, 2008.

2. A. Henandez and G. Weiss, A First Course on Wavelets, CRC Press, 1996.

Reference Books:

1. I. Daubechies , Ten Lectures on wavelets, SIAM, 1992.

2. M. A. Pinsky, Introduction to Fourier Analysis and Wavelets, GTM vol 102, AMS, 2008.

3. M. W. Frazier, An Introduction to Wavelets through Linear Algebra, Springer, 1999.

4. K. Groechenig, A Foundation of Time-Frequency Analysis, Springer, 2001.