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Wavelets and Applications

Prof. CS Sastry · IIT Hyderabad

Start with lecture 1 At NPTEL

About

Wavelets are localized and oscillatory functions that generate bases for several function spaces. The multiresolution framework, meant for constructing wavelets, possesses attractive numerical properties for executing the wavelet decomposition of a function. The course aims at discussing orthogonal/non-orthogonal wavelet bases constructed for the space of square integrable functions. It then discusses the algorithmic as well as the application of discrete wavelets.

Intended audience: Senior UG, M.Sc(Mathematics), M.Tech/PhD (Communication and Computer Science) students

Prerequisites: Basic functional analysis

Lectures

Week 1

  1. Basic functional analysis YouTube
  2. Fourier Series YouTube
  3. Fourier Transform-I (Fourier Integrals) YouTube
  4. Fourier Transform-II (Fourier transform) YouTube
  5. Fourier Transform-III (Motivations for Wavelets) YouTube

Week 2

  1. Continuous Wavelet transform-I YouTube
  2. Continuous Wavelet transform-II YouTube
  3. Frames-1 || Basics of frames, tight frames YouTube
  4. Frames-2 || General frames, reconstruction YouTube

Week 3

  1. Frames-3 (Frame operator and reconstruction) YouTube
  2. Frames-4 (Dual frames and their properties) YouTube
  3. Frames-5 (Approximate representation of dual frame members) YouTube
  4. Frames-6 (Frames of wavelets, Conditions on wavelets for frame property) YouTube
  5. Frames-7 (Frames of wavelets, Dual frames of wavelets YouTube

Week 4

  1. Riesz bases-1 YouTube
  2. Riesz bases-2 YouTube
  3. Riesz bases-3 YouTube
  4. Riesz bases-4 YouTube

Week 5

  1. Multiresolution Analysis-1 YouTube
  2. Multiresolution Analysis-2 YouTube
  3. Multiresolution Analysis-3 YouTube
  4. Multiresolution Analysis-4 YouTube

Week 6

  1. Wavelets from MRA-1 YouTube
  2. Wavelets from MRA-2 YouTube
  3. Wavelets from MRA-3 YouTube
  4. Wavelets from MRA-4 YouTube

Week 7

  1. Scaling functions for MRA-1 YouTube
  2. Scaling functions for MRA-2 YouTube
  3. Scaling functions for MRA-3 YouTube
  4. Scaling functions for MRA-4 YouTube

Week 8

  1. Scaling functions for MRA-5 YouTube
  2. Scaling functions for MRA-6 YouTube
  3. Scaling functions for MRA-7 YouTube
  4. Scaling functions for MRA-8 YouTube
  5. Scaling functions for MRA-9 YouTube

Week 9

  1. Computational aspects of wavelets-1 YouTube
  2. Computational aspects of wavelets-2 YouTube
  3. Computational aspects of wavelets-3 YouTube
  4. Computational aspects of wavelets-4 YouTube

Week 10

  1. Smoothness of MRA wavelets YouTube
  2. Other wavelet constructions -1 YouTube
  3. Other wavelet constructions -2 YouTube

Week 11

  1. Multidimensional wavelets-1 YouTube
  2. Multidimensional wavelets-2 YouTube
  3. A wavelet tour of MATLAB YouTube

Week 12

  1. Application of wavelets-1 YouTube
  2. Application of wavelets-2 YouTube
  3. Recent developments YouTube
  4. Summary of the contents covered in the course YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Hyderabad
Department
Mathematics
Teacher
Prof. CS Sastry
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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