Unit-I

Basic Properties of the Discrete Fourier Transform, Translation-Invariant Linear Transformations. The Fast Fourier Transform.

Unit-II

Construction of Wavelets on , The First Stage Construction of Wavelets on , The Iteration Step`s. Examples and Applications.

Unit-III

Complete Orthonormal Sets in Hilbert Spaces, and Fourier Series, The Fourier Transform and Convolution on First-Stage Wavelets on .
The Iteration Step for Wavelets on Z , Implementation and Examples.

Unit-IV

L2(R) and Approximate Identities, The Fourier Transform on , Multiresolution Analysis and Wavelets.

Unit-V

Construction of Multiresolution Analyses, Wavelets with Compact Support and Their Computation.

CO1 Understand and apply the concepts of DFT and its significance in Engineering problems
CO2 Understand and apply the concept of first stage wavelet basis and iterative stages of wavelet bases in finite dimensional space.
CO3 Understand and apply the concept of first stage wavelet basis and iterative stages of wavelet bases in infinite dimensional space.
CO4 Understand the concepts of Fourier transform and MRA and the construction of wavelets and its applications.

Text Books:

1. Michael W. Frazier, An Introduction to Wavelets Through Linear Algebra, Springer,1999.

References:

1. Daubechis, Ten Lectures on Wavelets, SIAM, 1992.
2. S. Mallat, A Wavelet Tour of Signal Processing, Elsevier, 2008.