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Course10810109371 lectures

Fundamentals of Wavelets, Filter Banks and Time Frequency Analysis

Prof. V. M. Gadre · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Module 1: Lecture 1: Introduction Video
  2. Module 1: Lecture 2: Origin of Wavelets Video
  3. Module 1: Lecture 3: Haar Wavelet Video
  4. Module 2: Lecture 1: Dyadic Wavelet Video
  5. Module 2: Lecture 2: Dilates and Translates of Haar Wavelets Video
  6. Module 2: Lecture 3: L2 Norm of a Function Video
  7. Module 3: Lecture 1: Piecewise Constant Representation of a Function Video
  8. Module 3: Lecture 2: Ladder of Subspaces Video
  9. Module 3: Lecture 3: Scaling Function for Haar Wavelet Demo Video
  10. Demonstration 1: Piecewise constant approximation of functions Video

Week 2

  1. Module 4: Lecture 1: Vector Representation of Sequences Video
  2. Module 4: Lecture 2: Properties of Norm Video
  3. Module 4: Lecture 3: Parseval's Theorem Video
  4. Module 5: Lecture 1: Equivalence of sequences and functions Video
  5. Module 5: Lecture 2: Angle between Functions & their Decomposition Video
  6. Demonstration 2: Additional Information on Direct-Sum Video
  7. Module 6: Lecture 1: Introduction to filter banks Video
  8. Module 6: Lecture 2: Haar Analysis Filter Bank in Z-domain Video
  9. Module 6: Lecture 3: Haar Synthesis Filter Bank in Z-domain Video
  10. Module 7: Lecture 1: Moving from Z-domain to frequency domain Video
  11. Module 7: Lecture 2: Frequency Response of Haar Analysis Low pass Filter bank Video
  12. Module 7: Lecture 3: Frequency Response of Haar Analysis High pass Filter bank Video

Week 3

  1. Module 8: Lecture 1: Ideal two-band filter bank Video
  2. Module 8: Lecture 2: Disqualification of Ideal filter bank Video
  3. Module 8: Lecture 3: Realizable two-band filter bank Video
  4. Demonstration 3: Demonstration: DWT of images Video
  5. Module 9: Lecture 1: Relating Fourier transform of scaling function to filter bank Video
  6. Module 9: Lecture 2: Fourier transform of scaling function Video
  7. Module 9: Lecture 3: Construction of scaling and wavelet functions from filter bank Video
  8. Demonstration 4: Demonstration: Constructing scaling and wavelet functions Video
  9. Module 10: Lecture 1: Introduction to upsampling and down sampling as Multirate operations Video
  10. Module 10: Lecture 2: Up sampling by a general factor M- a Z-domain analysis. Video
  11. Module 10: Lecture 3: Down sampling by a general factor M- a Z-domain analysis Video

Week 4

  1. Module 11: Lecture 1: Z domain analysis of 2 channel filter bank. Video
  2. Module 11: Lecture 2: Effect of X (-Z) in time domain and aliasing Video
  3. Module 11: Lecture 3: Consequences of aliasing and simple approach to avoid it Video
  4. Module 12: Lecture 1: Revisiting aliasing and the Idea of perfect reconstruction Video
  5. Module 12: Lecture 2: Applying perfect reconstruction and alias cancellation on Haar MRA Video
  6. Module 12: Lecture 3: Introduction to Daubechies family of MRA Video

Week 5

  1. Module 13: Lecture 1: Power Complementarity of low pass filter Video
  2. Module 13: Lecture 2: Applying perfect reconstruction condition to obtain filter coefficient Video
  3. Module 14: Lecture 1: Effect of minimum phase requirement on filter coefficients Video
  4. Module 14: Lecture 2: Building compactly supported scaling functions Video
  5. Module 14: Lecture 3: Second member of Daubechies family Video

Week 6

  1. Module 15: Lecture 1: Fourier transform analysis of Haar scaling and Wavelet functions Video
  2. Module 15: Lecture 2: Revisiting Fourier Transform and Parseval's theorem Video
  3. Module 15: Lecture 3: Transform Analysis of Haar Wavelet function Video
  4. Module 16: Lecture 1: Nature of Haar scaling and Wavelet functions in frequency domain Video
  5. Module 16: Lecture 2: The Idea of Time-Frequency Resolution Video
  6. Module 16: Lecture 3: Some thoughts on Ideal time- frequency domain behavior Video

Week 7

  1. Module 17: Lecture 1: Defining Probability Density function Video
  2. Module 17: Lecture 2: Defining Mean, Variance and “containment in a given domain” Video
  3. Module 17: Lecture 3: Example: Haar Scaling function Video
  4. Module 17: Lecture 4: Variance from a slightly different perspective Video
  5. Module 18: Lecture 1: Signal transformations: effect on mean and variance Video
  6. Module 18: Lecture 2: Time-Bandwidth product and its properties Video
  7. Module 18: Lecture 3: Simplification of Time-Bandwidth formulae Video
  8. Module 19: Lecture 1: Introduction Video
  9. Module 19: Lecture 2: Evaluation of Time-Bandwidth product Video
  10. Module 19: Lecture 3: Optimal function in the sense of Time-Bandwidth product Video

Week 8

  1. Module 20: Lecture 1: Discontent with the “Optimal function”. Video
  2. Module 20: Lecture 2: Journey from infinite to finite Time-Bandwidth product of Haar scaling function Video
  3. Module 20: Lecture 3: More insights about Time-Bandwidth product Video
  4. Module 20: Lecture 4: Time-frequency plane Video
  5. Module 20: Lecture 5: Tiling the Time-frequency plane Video
  6. Module 21: Lecture 1: STFT: Conditions for valid windows Video
  7. Module 21: Lecture 2: STFT: Time domain and frequency domain formulations Video
  8. Module 21: Lecture 3: STFT: Duality in the interpretations Video
  9. Module 21: Lecture 4: Continuous Wavelet Transform (CWT) Video
  10. Demonstration 5 Video
  11. Student’s Presentation Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Electrical Engineering
Teacher
Prof. V. M. Gadre
Level
Undergraduate
Language
English
Subjects
Engineering
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.
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