MSc (Mathematics and Computing) Programme:Wavelets and ApplicationsThapar University
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Real Analysis – I
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Based Management Systems
Computer Based Optimization Techniques
Wavelets and Applications
Different ways of constructing wavelets: Orthonormal bases generated by a single function; The Balian-low theorem. Smooth projections on L2(R). Local sine and cosine bases and the construction of some wavelets. The unitary folding operators and the smooth projections.
Multiresolution analysis: Multiresolution analysis and construction of wavelets. Construction of compactly supported wavelets and estimates for its smoothness. Band limited wavelets. Orthonormality. Completeness.
Characterizations in the theory of wavelets: The basic equations and some of its applications. Characterizations of MRA wavelets, Characterization of Lemarie-Meyer wavelets and some other characterizations. Franklin wavelets and spline wavelets on the real line. Orthonormal bases of piecewise linear continuous functions for L2(T). Orthonormal bases of periodization of wavelets defined on the real line.
Wavelets in Signal and Image Processing: Signals, Filters, coding signals, Filters banks, Image Analysis, Image Compression, Edge Detection.
Laboratory Work: Analysis of different wavelet filters, multiresolution analysis feature of different wavelets, Applications of wavelets in signal and image processing.