# Wavelets and Applications

- Institution: IIT Hyderabad
- Department: Mathematics
- Teacher: Prof. CS Sastry
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106002)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106002)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Basic functional analysis](https://invisiblenetwork.ai/learn/nptel/111106002/4159012d2edc) (YouTube)
2. [Fourier Series](https://invisiblenetwork.ai/learn/nptel/111106002/24774906e475) (YouTube)
3. [Fourier Transform-I (Fourier Integrals)](https://invisiblenetwork.ai/learn/nptel/111106002/eeae76e47dee) (YouTube)
4. [Fourier Transform-II (Fourier transform)](https://invisiblenetwork.ai/learn/nptel/111106002/7361481fc054) (YouTube)
5. [Fourier Transform-III (Motivations for Wavelets)](https://invisiblenetwork.ai/learn/nptel/111106002/07155452b99e) (YouTube)
6. [Continuous Wavelet transform-I](https://invisiblenetwork.ai/learn/nptel/111106002/98566133e318) (YouTube)
7. [Continuous Wavelet transform-II](https://invisiblenetwork.ai/learn/nptel/111106002/2c7f2aad9200) (YouTube)
8. [Frames-1 || Basics of frames, tight frames](https://invisiblenetwork.ai/learn/nptel/111106002/b239ef4564c4) (YouTube)
9. [Frames-2 || General frames, reconstruction](https://invisiblenetwork.ai/learn/nptel/111106002/a6cd2a02bb43) (YouTube)
10. [Frames-3 (Frame operator and reconstruction)](https://invisiblenetwork.ai/learn/nptel/111106002/feb966199d83) (YouTube)
11. [Frames-4 (Dual frames and their properties)](https://invisiblenetwork.ai/learn/nptel/111106002/4b749b97fc71) (YouTube)
12. [Frames-5 (Approximate representation of dual frame members)](https://invisiblenetwork.ai/learn/nptel/111106002/8d59dd3f1eb8) (YouTube)
13. [Frames-6 (Frames of wavelets, Conditions on wavelets for frame property)](https://invisiblenetwork.ai/learn/nptel/111106002/4ad96083a212) (YouTube)
14. [Frames-7 (Frames of wavelets, Dual frames of wavelets](https://invisiblenetwork.ai/learn/nptel/111106002/5da46065fc00) (YouTube)
15. [Riesz bases-1](https://invisiblenetwork.ai/learn/nptel/111106002/5147bf1787d3) (YouTube)
16. [Riesz bases-2](https://invisiblenetwork.ai/learn/nptel/111106002/ee096f73157c) (YouTube)
17. [Riesz bases-3](https://invisiblenetwork.ai/learn/nptel/111106002/15267ccb9203) (YouTube)
18. [Riesz bases-4](https://invisiblenetwork.ai/learn/nptel/111106002/49703343994e) (YouTube)
19. [Multiresolution Analysis-1](https://invisiblenetwork.ai/learn/nptel/111106002/6b5c32eeeed6) (YouTube)
20. [Multiresolution Analysis-2](https://invisiblenetwork.ai/learn/nptel/111106002/d74be73f66ab) (YouTube)
21. [Multiresolution Analysis-3](https://invisiblenetwork.ai/learn/nptel/111106002/80c1966ca178) (YouTube)
22. [Multiresolution Analysis-4](https://invisiblenetwork.ai/learn/nptel/111106002/a9b8d3c17f7f) (YouTube)
23. [Wavelets from MRA-1](https://invisiblenetwork.ai/learn/nptel/111106002/e65efcb937df) (YouTube)
24. [Wavelets from MRA-2](https://invisiblenetwork.ai/learn/nptel/111106002/9f2afd8605bc) (YouTube)
25. [Wavelets from MRA-3](https://invisiblenetwork.ai/learn/nptel/111106002/a6a7f43678cd) (YouTube)
26. [Wavelets from MRA-4](https://invisiblenetwork.ai/learn/nptel/111106002/378bd0cd12c7) (YouTube)
27. [Scaling functions for MRA-1](https://invisiblenetwork.ai/learn/nptel/111106002/ddca3c7855ae) (YouTube)
28. [Scaling functions for MRA-2](https://invisiblenetwork.ai/learn/nptel/111106002/99d9e24e7f97) (YouTube)
29. [Scaling functions for MRA-3](https://invisiblenetwork.ai/learn/nptel/111106002/d7a6802439a9) (YouTube)
30. [Scaling functions for MRA-4](https://invisiblenetwork.ai/learn/nptel/111106002/b98524a32a1d) (YouTube)
31. [Scaling functions for MRA-5](https://invisiblenetwork.ai/learn/nptel/111106002/971dc3516040) (YouTube)
32. [Scaling functions for MRA-6](https://invisiblenetwork.ai/learn/nptel/111106002/ed3ed4ff298e) (YouTube)
33. [Scaling functions for MRA-7](https://invisiblenetwork.ai/learn/nptel/111106002/73439196c4f5) (YouTube)
34. [Scaling functions for MRA-8](https://invisiblenetwork.ai/learn/nptel/111106002/03728b5a0901) (YouTube)
35. [Scaling functions for MRA-9](https://invisiblenetwork.ai/learn/nptel/111106002/cc372b05d2df) (YouTube)
36. [Computational aspects of wavelets-1](https://invisiblenetwork.ai/learn/nptel/111106002/b43d48a4301c) (YouTube)
37. [Computational aspects of wavelets-2](https://invisiblenetwork.ai/learn/nptel/111106002/dad6a43571c2) (YouTube)
38. [Computational aspects of wavelets-3](https://invisiblenetwork.ai/learn/nptel/111106002/8aff684fc93a) (YouTube)
39. [Computational aspects of wavelets-4](https://invisiblenetwork.ai/learn/nptel/111106002/bb491e506e95) (YouTube)
40. [Smoothness of MRA wavelets](https://invisiblenetwork.ai/learn/nptel/111106002/a448b965e971) (YouTube)
41. [Other wavelet constructions -1](https://invisiblenetwork.ai/learn/nptel/111106002/48c111e13363) (YouTube)
42. [Other wavelet constructions -2](https://invisiblenetwork.ai/learn/nptel/111106002/ea12ecae8dc9) (YouTube)
43. [Multidimensional wavelets-1](https://invisiblenetwork.ai/learn/nptel/111106002/c4a1e8df8b20) (YouTube)
44. [Multidimensional wavelets-2](https://invisiblenetwork.ai/learn/nptel/111106002/31ebfa052a8d) (YouTube)
45. [A wavelet tour of MATLAB](https://invisiblenetwork.ai/learn/nptel/111106002/df48af61a428) (YouTube)
46. [Application of wavelets-1](https://invisiblenetwork.ai/learn/nptel/111106002/e8b32a8977d5) (YouTube)
47. [Application of wavelets-2](https://invisiblenetwork.ai/learn/nptel/111106002/58dc773228cb) (YouTube)
48. [Recent developments](https://invisiblenetwork.ai/learn/nptel/111106002/64514962f214) (YouTube)
49. [Summary of the contents covered in the course](https://invisiblenetwork.ai/learn/nptel/111106002/748ad48e8f42) (YouTube)