# Foundations of Wavelets and Multirate Digital Signal Processing

- Institution: IIT Bombay
- Department: Electronics & Communication Engineering
- Teacher: Prof. V. M. Gadre
- Level: Undergraduate
- Language: English
- Subjects: Engineering, Society and politics
- Source: [NPTEL](https://nptel.ac.in/courses/117101123)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/117101123)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction](https://invisiblenetwork.ai/learn/nptel/117101123/7123f3466fc0) (Video)
2. [Origin of wavelets](https://invisiblenetwork.ai/learn/nptel/117101123/1f24b292bde1) (Video)
3. [Haar wavelet](https://invisiblenetwork.ai/learn/nptel/117101123/fe4e8067cd56) (Video)
4. [Dyadic wavelet](https://invisiblenetwork.ai/learn/nptel/117101123/cddb4087155c) (Video)
5. [Dilates and translates of Haar wavelet](https://invisiblenetwork.ai/learn/nptel/117101123/5719f37a1455) (Video)
6. [L2 norm of a function](https://invisiblenetwork.ai/learn/nptel/117101123/c6ba35d86957) (Video)
7. [Piecewise constant representation of a function](https://invisiblenetwork.ai/learn/nptel/117101123/38419889394a) (Video)
8. [Ladder of subspaces](https://invisiblenetwork.ai/learn/nptel/117101123/ac3abdaa0fd9) (Video)
9. [Scaling function of Haar wavelet](https://invisiblenetwork.ai/learn/nptel/117101123/920fae66e57c) (Video)
10. [Demonstration: Piecewise constant approximation of functions](https://invisiblenetwork.ai/learn/nptel/117101123/82794c3e158f) (Video)
11. [Vector representation of sequences](https://invisiblenetwork.ai/learn/nptel/117101123/99aa61294477) (Video)
12. [Properties of norm](https://invisiblenetwork.ai/learn/nptel/117101123/0aaa63e6ae37) (Video)
13. [Parsevals theorem](https://invisiblenetwork.ai/learn/nptel/117101123/8be589132261) (Video)
14. [Equivalence of functions & sequences](https://invisiblenetwork.ai/learn/nptel/117101123/c8cf3d33208e) (Video)
15. [Angle between Functions & their Decomposition](https://invisiblenetwork.ai/learn/nptel/117101123/976295cfcdb3) (Video)
16. [Additional Information on Direct-Sum](https://invisiblenetwork.ai/learn/nptel/117101123/eae6a54a26ba) (Video)
17. [Introduction to filter banks](https://invisiblenetwork.ai/learn/nptel/117101123/b8463c0b6cce) (Video)
18. [Haar Analysis filter bank in Z-domain](https://invisiblenetwork.ai/learn/nptel/117101123/56c84a1645db) (Video)
19. [Haar Synthesis filter bank in Z-domain](https://invisiblenetwork.ai/learn/nptel/117101123/01c7598c358d) (Video)
20. [Moving from Z-domain to frequency domain](https://invisiblenetwork.ai/learn/nptel/117101123/17c8815c748c) (Video)
21. [Frequency Response of Haar Analysis Low pass Filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/de07c7eacc1e) (Video)
22. [Frequency Response of Haar Analysis High pass Filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/56e13b13f6c4) (Video)
23. [Ideal Two-band Filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/ce96b03085f1) (Video)
24. [Disqualification of Ideal Filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/542f8801b948) (Video)
25. [Realizable Two-band Filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/edf45b30ce1c) (Video)
26. [Demonstration: DWT of images](https://invisiblenetwork.ai/learn/nptel/117101123/901e1eedf39b) (Video)
27. [Relating Fourier transform of scaling function to filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/a07f1d4cbcca) (Video)
28. [Fourier transform of scaling function](https://invisiblenetwork.ai/learn/nptel/117101123/a83565987cfc) (Video)
29. [Construction of scaling and wavelet functions from filter bank](https://invisiblenetwork.ai/learn/nptel/117101123/959ba4727e4c) (Video)
30. [Demonstration: Constructing scaling and wavelet functions.](https://invisiblenetwork.ai/learn/nptel/117101123/9e914b540f3d) (Video)
31. [Conclusive Remarks and Future Prospects](https://invisiblenetwork.ai/learn/nptel/117101123/88de22c8770c) (Video)
32. [Live Session 20-02-2024](https://invisiblenetwork.ai/learn/nptel/117101123/7123f3466fc0-2) (Video)
33. [Live Session 21-02-2025](https://invisiblenetwork.ai/learn/nptel/117101123/1f24b292bde1-2) (Video)