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Course11710112333 lectures

Foundations of Wavelets and Multirate Digital Signal Processing

Prof. V. M. Gadre · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Introduction Video
  2. Origin of wavelets Video
  3. Haar wavelet Video
  4. Dyadic wavelet Video
  5. Dilates and translates of Haar wavelet Video
  6. L2 norm of a function Video

Week 2

  1. Piecewise constant representation of a function Video
  2. Ladder of subspaces Video
  3. Scaling function of Haar wavelet Video
  4. Demonstration: Piecewise constant approximation of functions Video
  5. Vector representation of sequences Video
  6. Properties of norm Video
  7. Parsevals theorem Video

Week 3

  1. Equivalence of functions & sequences Video
  2. Angle between Functions & their Decomposition Video
  3. Additional Information on Direct-Sum Video
  4. Introduction to filter banks Video
  5. Haar Analysis filter bank in Z-domain Video
  6. Haar Synthesis filter bank in Z-domain Video

Week 4

  1. Moving from Z-domain to frequency domain Video
  2. Frequency Response of Haar Analysis Low pass Filter bank Video
  3. Frequency Response of Haar Analysis High pass Filter bank Video
  4. Ideal Two-band Filter bank Video
  5. Disqualification of Ideal Filter bank Video
  6. Realizable Two-band Filter bank Video
  7. Demonstration: DWT of images Video

Week 5

  1. Relating Fourier transform of scaling function to filter bank Video
  2. Fourier transform of scaling function Video
  3. Construction of scaling and wavelet functions from filter bank Video
  4. Demonstration: Constructing scaling and wavelet functions. Video
  5. Conclusive Remarks and Future Prospects Video

Live Session

  1. Live Session 20-02-2024 Video
  2. Live Session 21-02-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Electronics & Communication Engineering
Teacher
Prof. V. M. Gadre
Level
Undergraduate
Language
English
Subjects
Engineering, Society and politics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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