# Mathematical Methods and Techniques in Signal Processing

- Institution: IISc Bangalore
- Department: Electrical Engineering
- Teacher: Prof. Shayan Srinivasa Garani
- Level: Graduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108108109)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108108109)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Review of basic signals, systems and signal space: Review of 1-D signals and systems, review of random signals, multi-dimensional signals, review of vector spaces, inner product spaces, orthogonal projections and related concepts.

Sampling theorems (a peek into Shannon and compressive sampling), Basics of multi-rate signal processing: sampling, decimation and interpolation, sampling rate conversion (integer and rational sampling rates), oversampled processing (A/D and D/A conversion), and introduction to filter banks.

Signal representation: Transform theory and methods (FT and variations, KLT), other transform methods including convergence issues.

Wavelets: Characterization of wavelets, wavelet transform, multi-resolution analysis.

Intended audience: Post graduates and senior UGs with a strong background in basic DSP.PRE-REQUISITES : UG in Digital Signal Processing, familiarity with probability and linear algebra

## Lectures

1. [Introduction to signal processing](https://invisiblenetwork.ai/learn/nptel/108108109/2910a5b219cd) (YouTube)
2. [Basics of signals and systems](https://invisiblenetwork.ai/learn/nptel/108108109/c72891befeba) (YouTube)
3. [Linear time-invariant systems](https://invisiblenetwork.ai/learn/nptel/108108109/2d6df6be23ab) (YouTube)
4. [Modes in a linear system](https://invisiblenetwork.ai/learn/nptel/108108109/e350974945c3) (YouTube)
5. [Introduction to state space representation](https://invisiblenetwork.ai/learn/nptel/108108109/a05ddb3f1996) (YouTube)
6. [State space representation](https://invisiblenetwork.ai/learn/nptel/108108109/f2ca4edacf60) (YouTube)
7. [Non-uniqueness of state space representation](https://invisiblenetwork.ai/learn/nptel/108108109/bfe1b7489ec6) (YouTube)
8. [Introduction to vector space](https://invisiblenetwork.ai/learn/nptel/108108109/2709a224cb3a) (YouTube)
9. [Linear independence and spanning set](https://invisiblenetwork.ai/learn/nptel/108108109/fbaa7eef8e0d) (YouTube)
10. [Unique representation theorem](https://invisiblenetwork.ai/learn/nptel/108108109/29f3359285b1) (YouTube)
11. [Basis and cardinality of basis](https://invisiblenetwork.ai/learn/nptel/108108109/e4c2e242ce8a) (YouTube)
12. [Norms and inner product spaces](https://invisiblenetwork.ai/learn/nptel/108108109/372a13891136) (YouTube)
13. [Inner products and induced norm](https://invisiblenetwork.ai/learn/nptel/108108109/3a9d2c478a17) (YouTube)
14. [Cauchy Schwartz inequality](https://invisiblenetwork.ai/learn/nptel/108108109/1bc247723736) (YouTube)
15. [Orthonormality](https://invisiblenetwork.ai/learn/nptel/108108109/c21bfdd0b05e) (YouTube)
16. [Problem on sum of subspaces](https://invisiblenetwork.ai/learn/nptel/108108109/8febc58de0f1) (YouTube)
17. [Linear independence of orthogonal vectors](https://invisiblenetwork.ai/learn/nptel/108108109/dee0f6079843) (YouTube)
18. [Hilbert space and linear transformation](https://invisiblenetwork.ai/learn/nptel/108108109/1699f6612401) (YouTube)
19. [Gram Schmidt orthonormalization](https://invisiblenetwork.ai/learn/nptel/108108109/f4f9eedee4af) (YouTube)
20. [Linear approximation of signal space](https://invisiblenetwork.ai/learn/nptel/108108109/17337b39c498) (YouTube)
21. [Gram Schmidt orthogonalization of signals](https://invisiblenetwork.ai/learn/nptel/108108109/75d156af2d44) (YouTube)
22. [Problem on orthogonal complement](https://invisiblenetwork.ai/learn/nptel/108108109/85b94c791c9f) (YouTube)
23. [Problem on signal geometry (4-QAM)](https://invisiblenetwork.ai/learn/nptel/108108109/c4ed164f76fd) (YouTube)
24. [Basics of probability and random variables](https://invisiblenetwork.ai/learn/nptel/108108109/78706a54422f) (YouTube)
25. [Mean and variance of a random variable](https://invisiblenetwork.ai/learn/nptel/108108109/18e11822f13c) (YouTube)
26. [Introduction to random process](https://invisiblenetwork.ai/learn/nptel/108108109/c8699cd7d738) (YouTube)
27. [Statistical specification of random processes](https://invisiblenetwork.ai/learn/nptel/108108109/0a99e8bfa136) (YouTube)
28. [Stationarity of random processes](https://invisiblenetwork.ai/learn/nptel/108108109/8558654e5498) (YouTube)
29. [Problem on mean and variance](https://invisiblenetwork.ai/learn/nptel/108108109/f693d2d09da2) (YouTube)
30. [Problem on MAP Detection](https://invisiblenetwork.ai/learn/nptel/108108109/7f566a19639f) (YouTube)
31. [Fourier transform of dirac comb sequence](https://invisiblenetwork.ai/learn/nptel/108108109/7e28adc2bfa9) (YouTube)
32. [Sampling theorem](https://invisiblenetwork.ai/learn/nptel/108108109/e2932d68e00c) (YouTube)
33. [Basics of multirate systems](https://invisiblenetwork.ai/learn/nptel/108108109/1a47ea1e8dd9) (YouTube)
34. [Frequency representation of expanders and decimators](https://invisiblenetwork.ai/learn/nptel/108108109/9a8fd8e0e0a5) (YouTube)
35. [Decimation and interpolation filters](https://invisiblenetwork.ai/learn/nptel/108108109/a6d2401b1e12) (YouTube)
36. [Fractional sampling rate alterations](https://invisiblenetwork.ai/learn/nptel/108108109/80246f361288) (YouTube)
37. [Digital filter banks](https://invisiblenetwork.ai/learn/nptel/108108109/d3a205b08893) (YouTube)
38. [DFT as filter bank](https://invisiblenetwork.ai/learn/nptel/108108109/63d3a0643721) (YouTube)
39. [Noble Identities](https://invisiblenetwork.ai/learn/nptel/108108109/99e9971656f0) (YouTube)
40. [Polyphase representation](https://invisiblenetwork.ai/learn/nptel/108108109/5819a9fd33ea) (YouTube)
41. [Efficient architectures for interpolation and decimation filters](https://invisiblenetwork.ai/learn/nptel/108108109/e8779b220925) (YouTube)
42. [Problems on simplifying multirate systems using noble identities](https://invisiblenetwork.ai/learn/nptel/108108109/118199df9451) (YouTube)
43. [Problem on designing synthesis bank filters](https://invisiblenetwork.ai/learn/nptel/108108109/9ea3fe9fdfec) (YouTube)
44. [Efficient architecture for fractional decimator](https://invisiblenetwork.ai/learn/nptel/108108109/f3ce85ce43e9) (YouTube)
45. [Multistage filter design](https://invisiblenetwork.ai/learn/nptel/108108109/19246dff74b1) (YouTube)
46. [Two-channel filter banks](https://invisiblenetwork.ai/learn/nptel/108108109/13eb9f2f804f) (YouTube)
47. [Amplitude and phase distortion in signals](https://invisiblenetwork.ai/learn/nptel/108108109/20d2fe960fe1) (YouTube)
48. [Polyphase representation of 2-channel filter banks, signal flow graphs and perfect reconstruction](https://invisiblenetwork.ai/learn/nptel/108108109/58893542fabb) (YouTube)
49. [M-channel filter banks](https://invisiblenetwork.ai/learn/nptel/108108109/c06cc5e28caa) (YouTube)
50. [Polyphase representation of M-channel filter bank](https://invisiblenetwork.ai/learn/nptel/108108109/fc905fafde17) (YouTube)
51. [Perfect reconstruction of signals](https://invisiblenetwork.ai/learn/nptel/108108109/8a18fff74482) (YouTube)
52. [Nyquist and half band filters](https://invisiblenetwork.ai/learn/nptel/108108109/14721336ee4d) (YouTube)
53. [Special filter banks for perfect reconstruction](https://invisiblenetwork.ai/learn/nptel/108108109/627c6420c887) (YouTube)
54. [Introduction to wavelets](https://invisiblenetwork.ai/learn/nptel/108108109/fd64a6f1e10f) (YouTube)
55. [Multiresolution analysis and properties](https://invisiblenetwork.ai/learn/nptel/108108109/c0ac2c74f5c8) (YouTube)
56. [The Haar wavelet](https://invisiblenetwork.ai/learn/nptel/108108109/7fbc6451ae01) (YouTube)
57. [Structure of subspaces in MRA](https://invisiblenetwork.ai/learn/nptel/108108109/f4e2113c5f75) (YouTube)
58. [Haar decomposition - 1](https://invisiblenetwork.ai/learn/nptel/108108109/bbeab4bdf8f3) (YouTube)
59. [Haar decomposition - 2](https://invisiblenetwork.ai/learn/nptel/108108109/2a958ca28b99) (YouTube)
60. [Wavelet Reconstruction](https://invisiblenetwork.ai/learn/nptel/108108109/428af9156660) (YouTube)
61. [Haar wavelet and link to filter banks](https://invisiblenetwork.ai/learn/nptel/108108109/5fa6f643a4d9) (YouTube)
62. [Demo on wavelet decomposition](https://invisiblenetwork.ai/learn/nptel/108108109/8c78977337bb) (YouTube)
63. [Problem on circular convolution](https://invisiblenetwork.ai/learn/nptel/108108109/d490600a7950) (YouTube)
64. [Time frequency localization](https://invisiblenetwork.ai/learn/nptel/108108109/415c88d3bb96) (YouTube)
65. [Basic analysis: Pointwise and uniform continuity of functions](https://invisiblenetwork.ai/learn/nptel/108108109/798744b41a51) (YouTube)
66. [Basic Analysis : Convergence of sequence of functions](https://invisiblenetwork.ai/learn/nptel/108108109/f00fa3d62250) (YouTube)
67. [Fourier series and notions of convergence](https://invisiblenetwork.ai/learn/nptel/108108109/d3075c79a013) (YouTube)
68. [Convergence of Fourier series at a point of continuity](https://invisiblenetwork.ai/learn/nptel/108108109/9fcdc05f13b9) (YouTube)
69. [Convergence of Fourier series for piecewise differentiable periodic functions](https://invisiblenetwork.ai/learn/nptel/108108109/1c5240069330) (YouTube)
70. [Uniform convergence of Fourier series of piecewise smooth periodic function](https://invisiblenetwork.ai/learn/nptel/108108109/25964b3951d3) (YouTube)
71. [Convergence in norm of Fourier series](https://invisiblenetwork.ai/learn/nptel/108108109/e070e2e032ae) (YouTube)
72. [Convergence of Fourier series for all square integrable periodic functions](https://invisiblenetwork.ai/learn/nptel/108108109/2c6a3084532c) (YouTube)
73. [Problem on limits of integration of periodic functions](https://invisiblenetwork.ai/learn/nptel/108108109/d9ba758a9e62) (YouTube)
74. [Matrix Calculus](https://invisiblenetwork.ai/learn/nptel/108108109/e2c70d05f2db) (YouTube)
75. [KL transform](https://invisiblenetwork.ai/learn/nptel/108108109/48e2ede56712) (YouTube)
76. [Applications of KL transform](https://invisiblenetwork.ai/learn/nptel/108108109/6cc943b1373c) (YouTube)
77. [Demo on KL Transform](https://invisiblenetwork.ai/learn/nptel/108108109/236056bff8d3) (YouTube)