<h3>MA6003 Theory of Wavelets (modified)</h3>
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<h4>Course Details</h4>
Unit 1: A quick review of Fourier series in L<sup>2</sup>(T) and Fourier transform on L<sup>2</sup>(R), Genesis of Wavelets, Short time Fourier transform, Properties and Orthogonality relation, Inversion formula Continuous wavelet transform, Orthogonality relation and Inversion formula (13 lectures)<br><br> Unit 2: Discretization, Frames and Riesz bases, Frame operators, Gabor frames and Wavelet frames, Balian-Low theorem (12 lectures)<br><br> 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)
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<h4>Course References:</h4>
Text Books:<br>
1. O. Christensen, Frames and Bases : An Introductory Course, Springer, 2008.<br>
2. A. Henandez and G. Weiss, A First Course on Wavelets, CRC Press, 1996.<br><br>
Reference Books:<br>
1. I. Daubechies , Ten Lectures on wavelets, SIAM, 1992.<br>
2. M. A. Pinsky, Introduction to Fourier Analysis and Wavelets, GTM vol 102, AMS, 2008.<br>
3. M. W. Frazier, An Introduction to Wavelets through Linear Algebra, Springer, 1999.<br>
4. K. Groechenig, A Foundation of Time-Frequency Analysis, Springer, 2001.