# Fundamentals of Wavelets, Filter Banks and Time Frequency Analysis

- Institution: IIT Bombay
- Department: Electrical Engineering
- Teacher: Prof. V. M. Gadre
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108101093)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108101093)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Module 1: Lecture 1: Introduction](https://invisiblenetwork.ai/learn/nptel/108101093/a1ed5a45d983) (Video)
2. [Module 1: Lecture 2: Origin of Wavelets](https://invisiblenetwork.ai/learn/nptel/108101093/7df6ee93fe36) (Video)
3. [Module 1: Lecture 3: Haar Wavelet](https://invisiblenetwork.ai/learn/nptel/108101093/80c8cba2d6e8) (Video)
4. [Module 2: Lecture 1: Dyadic Wavelet](https://invisiblenetwork.ai/learn/nptel/108101093/5ee1459f5bb2) (Video)
5. [Module 2: Lecture 2: Dilates and Translates of Haar Wavelets](https://invisiblenetwork.ai/learn/nptel/108101093/35aa591f8216) (Video)
6. [Module 2: Lecture 3: L2 Norm of a Function](https://invisiblenetwork.ai/learn/nptel/108101093/a4e64ba0408e) (Video)
7. [Module 3: Lecture 1: Piecewise Constant Representation of a Function](https://invisiblenetwork.ai/learn/nptel/108101093/24345f8f59d3) (Video)
8. [Module 3: Lecture 2: Ladder of Subspaces](https://invisiblenetwork.ai/learn/nptel/108101093/8e4d7a191da9) (Video)
9. [Module 3: Lecture 3: Scaling Function for Haar Wavelet Demo](https://invisiblenetwork.ai/learn/nptel/108101093/2ea0e129eb53) (Video)
10. [Demonstration 1: Piecewise constant approximation of functions](https://invisiblenetwork.ai/learn/nptel/108101093/9c31049e9345) (Video)
11. [Module 4: Lecture 1: Vector Representation of Sequences](https://invisiblenetwork.ai/learn/nptel/108101093/06809550ae2d) (Video)
12. [Module 4: Lecture 2: Properties of Norm](https://invisiblenetwork.ai/learn/nptel/108101093/98bb732a560d) (Video)
13. [Module 4: Lecture 3: Parseval's Theorem](https://invisiblenetwork.ai/learn/nptel/108101093/9c85129114e3) (Video)
14. [Module 5: Lecture 1: Equivalence of sequences and functions](https://invisiblenetwork.ai/learn/nptel/108101093/e4052cf1cf46) (Video)
15. [Module 5: Lecture 2: Angle between Functions & their Decomposition](https://invisiblenetwork.ai/learn/nptel/108101093/f6ad72b088ce) (Video)
16. [Demonstration 2: Additional Information on Direct-Sum](https://invisiblenetwork.ai/learn/nptel/108101093/edf2f61466f2) (Video)
17. [Module 6: Lecture 1: Introduction to filter banks](https://invisiblenetwork.ai/learn/nptel/108101093/9cf19676a182) (Video)
18. [Module 6: Lecture 2: Haar Analysis Filter Bank in Z-domain](https://invisiblenetwork.ai/learn/nptel/108101093/dbb6da3de250) (Video)
19. [Module 6: Lecture 3: Haar Synthesis Filter Bank in Z-domain](https://invisiblenetwork.ai/learn/nptel/108101093/a1736d2fea92) (Video)
20. [Module 7: Lecture 1: Moving from Z-domain to frequency domain](https://invisiblenetwork.ai/learn/nptel/108101093/decb78f1e817) (Video)
21. [Module 7: Lecture 2: Frequency Response of Haar Analysis Low pass Filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/7660cf38ea92) (Video)
22. [Module 7: Lecture 3: Frequency Response of Haar Analysis High pass Filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/67c1504fe048) (Video)
23. [Module 8: Lecture 1: Ideal two-band filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/d2282da86ccc) (Video)
24. [Module 8: Lecture 2: Disqualification of Ideal filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/7576f6b33bd5) (Video)
25. [Module 8: Lecture 3: Realizable two-band filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/8339cf0c107f) (Video)
26. [Demonstration 3: Demonstration: DWT of images](https://invisiblenetwork.ai/learn/nptel/108101093/e1f206b60d93) (Video)
27. [Module 9: Lecture 1: Relating Fourier transform of scaling function to filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/1aa76c899a27) (Video)
28. [Module 9: Lecture 2: Fourier transform of scaling function](https://invisiblenetwork.ai/learn/nptel/108101093/218c0a64e9a1) (Video)
29. [Module 9: Lecture 3: Construction of scaling and wavelet functions from filter bank](https://invisiblenetwork.ai/learn/nptel/108101093/1ce38a0bf13e) (Video)
30. [Demonstration 4: Demonstration: Constructing scaling and wavelet functions](https://invisiblenetwork.ai/learn/nptel/108101093/a2e5491ee6b0) (Video)
31. [Module 10: Lecture 1: Introduction to upsampling and down sampling as Multirate operations](https://invisiblenetwork.ai/learn/nptel/108101093/335cd2d7ebe9) (Video)
32. [Module 10: Lecture 2: Up sampling by a general factor M- a Z-domain analysis.](https://invisiblenetwork.ai/learn/nptel/108101093/491eb4567af8) (Video)
33. [Module 10: Lecture 3: Down sampling by a general factor M- a Z-domain analysis](https://invisiblenetwork.ai/learn/nptel/108101093/d863de68dfbe) (Video)
34. [Module 11: Lecture 1: Z domain analysis of 2 channel filter bank.](https://invisiblenetwork.ai/learn/nptel/108101093/2bc7c351fea3) (Video)
35. [Module 11: Lecture 2: Effect of X (-Z) in time domain and aliasing](https://invisiblenetwork.ai/learn/nptel/108101093/023362ff8a5e) (Video)
36. [Module 11: Lecture 3: Consequences of aliasing and simple approach to avoid it](https://invisiblenetwork.ai/learn/nptel/108101093/a9a4e8d07a5e) (Video)
37. [Module 12: Lecture 1: Revisiting aliasing and the Idea of perfect reconstruction](https://invisiblenetwork.ai/learn/nptel/108101093/428d7548624e) (Video)
38. [Module 12: Lecture 2: Applying perfect reconstruction and alias cancellation on Haar MRA](https://invisiblenetwork.ai/learn/nptel/108101093/55e941a7c29d) (Video)
39. [Module 12: Lecture 3: Introduction to Daubechies family of MRA](https://invisiblenetwork.ai/learn/nptel/108101093/6aa4deb56d12) (Video)
40. [Module 13: Lecture 1: Power Complementarity of low pass filter](https://invisiblenetwork.ai/learn/nptel/108101093/dd1e2d7f0dbd) (Video)
41. [Module 13: Lecture 2: Applying perfect reconstruction condition to obtain filter coefficient](https://invisiblenetwork.ai/learn/nptel/108101093/6825412553de) (Video)
42. [Module 14: Lecture 1: Effect of minimum phase requirement on filter coefficients](https://invisiblenetwork.ai/learn/nptel/108101093/15d474f61a74) (Video)
43. [Module 14: Lecture 2: Building compactly supported scaling functions](https://invisiblenetwork.ai/learn/nptel/108101093/3763a2f1b654) (Video)
44. [Module 14: Lecture 3: Second member of Daubechies family](https://invisiblenetwork.ai/learn/nptel/108101093/e199bc1d41de) (Video)
45. [Module 15: Lecture 1: Fourier transform analysis of Haar scaling and Wavelet functions](https://invisiblenetwork.ai/learn/nptel/108101093/7b8a3ed6039b) (Video)
46. [Module 15: Lecture 2: Revisiting Fourier Transform and Parseval's theorem](https://invisiblenetwork.ai/learn/nptel/108101093/2c7ddfb8e618) (Video)
47. [Module 15: Lecture 3: Transform Analysis of Haar Wavelet function](https://invisiblenetwork.ai/learn/nptel/108101093/87949a633bd3) (Video)
48. [Module 16: Lecture 1: Nature of Haar scaling and Wavelet functions in frequency domain](https://invisiblenetwork.ai/learn/nptel/108101093/9fd25862cda7) (Video)
49. [Module 16: Lecture 2: The Idea of Time-Frequency Resolution](https://invisiblenetwork.ai/learn/nptel/108101093/896f6c0b14e6) (Video)
50. [Module 16: Lecture 3: Some thoughts on Ideal time- frequency domain behavior](https://invisiblenetwork.ai/learn/nptel/108101093/66274759711c) (Video)
51. [Module 17: Lecture 1: Defining Probability Density function](https://invisiblenetwork.ai/learn/nptel/108101093/56e3b03d624b) (Video)
52. [Module 17: Lecture 2: Defining Mean, Variance and “containment in a given domain”](https://invisiblenetwork.ai/learn/nptel/108101093/d5cbca17ec5f) (Video)
53. [Module 17: Lecture 3: Example: Haar Scaling function](https://invisiblenetwork.ai/learn/nptel/108101093/2684a260b17a) (Video)
54. [Module 17: Lecture 4: Variance from a slightly different perspective](https://invisiblenetwork.ai/learn/nptel/108101093/d7a7c1702f09) (Video)
55. [Module 18: Lecture 1: Signal transformations: effect on mean and variance](https://invisiblenetwork.ai/learn/nptel/108101093/7808dc691f6c) (Video)
56. [Module 18: Lecture 2: Time-Bandwidth product and its properties](https://invisiblenetwork.ai/learn/nptel/108101093/cf9a7d8e9c72) (Video)
57. [Module 18: Lecture 3: Simplification of Time-Bandwidth formulae](https://invisiblenetwork.ai/learn/nptel/108101093/c2683bf81bac) (Video)
58. [Module 19: Lecture 1: Introduction](https://invisiblenetwork.ai/learn/nptel/108101093/2c764003c4f0) (Video)
59. [Module 19: Lecture 2: Evaluation of Time-Bandwidth product](https://invisiblenetwork.ai/learn/nptel/108101093/aeafe603c3ad) (Video)
60. [Module 19: Lecture 3: Optimal function in the sense of Time-Bandwidth product](https://invisiblenetwork.ai/learn/nptel/108101093/d873eb2429ef) (Video)
61. [Module 20: Lecture 1: Discontent with the “Optimal function”.](https://invisiblenetwork.ai/learn/nptel/108101093/8598dbb34baa) (Video)
62. [Module 20: Lecture 2: Journey from infinite to finite Time-Bandwidth product of Haar scaling function](https://invisiblenetwork.ai/learn/nptel/108101093/f5b89fa7e1e1) (Video)
63. [Module 20: Lecture 3: More insights about Time-Bandwidth product](https://invisiblenetwork.ai/learn/nptel/108101093/19c34fa5e43e) (Video)
64. [Module 20: Lecture 4: Time-frequency plane](https://invisiblenetwork.ai/learn/nptel/108101093/e04f3e540b37) (Video)
65. [Module 20: Lecture 5: Tiling the Time-frequency plane](https://invisiblenetwork.ai/learn/nptel/108101093/342ac4a6c0b5) (Video)
66. [Module 21: Lecture 1: STFT: Conditions for valid windows](https://invisiblenetwork.ai/learn/nptel/108101093/7c799e8b6e1d) (Video)
67. [Module 21: Lecture 2: STFT: Time domain and frequency domain formulations](https://invisiblenetwork.ai/learn/nptel/108101093/41d71468a864) (Video)
68. [Module 21: Lecture 3: STFT: Duality in the interpretations](https://invisiblenetwork.ai/learn/nptel/108101093/4d9378409219) (Video)
69. [Module 21: Lecture 4: Continuous Wavelet Transform (CWT)](https://invisiblenetwork.ai/learn/nptel/108101093/efd4dcf98e87) (Video)
70. [Demonstration 5](https://invisiblenetwork.ai/learn/nptel/108101093/8fd2f28c3702) (Video)
71. [Student’s Presentation](https://invisiblenetwork.ai/learn/nptel/108101093/ecc58fda1d49) (Video)