NOC:Mathematical Methods and Techniques in Signal Processing


Lecture 1 - Introduction to signal processing


Lecture 2 - Basics of signals and systems


Lecture 3 - Linear time-invariant systems


Lecture 4 - Modes in a linear system


Lecture 5 - Introduction to state space representation


Lecture 6 - State space representation


Lecture 7 - Non-uniqueness of state space representation


Lecture 8 - Introduction to vector space


Lecture 9 - Linear independence and spanning set


Lecture 10 - Unique representation theorem


Lecture 11 - Basis and cardinality of basis


Lecture 12 - Norms and inner product spaces


Lecture 13 - Inner products and induced norm


Lecture 14 - Cauchy Schwartz inequality


Lecture 15 - Orthonormality


Lecture 16 - Problem on sum of subspaces


Lecture 17 - Linear independence of orthogonal vectors


Lecture 18 - Hilbert space and linear transformation


Lecture 19 - Gram Schmidt orthonormalization


Lecture 20 - Linear approximation of signal space


Lecture 21 - Gram Schmidt orthogonalization of signals


Lecture 22 - Problem on orthogonal complement


Lecture 23 - Problem on signal geometry (4-QAM)


Lecture 24 - Basics of probability and random variables


Lecture 25 - Mean and variance of a random variable


Lecture 26 - Introduction to random process


Lecture 27 - Statistical specification of random processes


Lecture 28 - Stationarity of random processes


Lecture 29 - Problem on mean and variance


Lecture 30 - Problem on MAP Detection


Lecture 31 - Fourier transform of dirac comb sequence


Lecture 32 - Sampling theorem


Lecture 33 - Basics of multirate systems


Lecture 34 - Frequency representation of expanders and decimators


Lecture 35 - Decimation and interpolation filters


Lecture 36 - Fractional sampling rate alterations


Lecture 37 - Digital filter banks


Lecture 38 - DFT as filter bank


Lecture 39 - Noble Identities


Lecture 40 - Polyphase representation


Lecture 41 - Efficient architectures for interpolation and decimation filters


Lecture 42 - Problems on simplifying multirate systems using noble identities


Lecture 43 - Problem on designing synthesis bank filters


Lecture 44 - Efficient architecture for fractional decimator


Lecture 45 - Multistage filter design


Lecture 46 - Two-channel filter banks


Lecture 47 - Amplitude and phase distortion in signals


Lecture 48 - Polyphase representation of 2-channel filter banks, signal flow graphs and perfect reconstruction


Lecture 49 - M-channel filter banks


Lecture 50 - Polyphase representation of M-channel filter bank


Lecture 51 - Perfect reconstruction of signals


Lecture 52 - Nyquist and half band filters


Lecture 53 - Special filter banks for perfect reconstruction


Lecture 54 - Introduction to wavelets


Lecture 55 - Multiresolution analysis and properties


Lecture 56 - The Haar wavelet


Lecture 57 - Structure of subspaces in MRA


Lecture 58 - Haar decomposition - 1


Lecture 59 - Haar decomposition - 2


Lecture 60 - Wavelet Reconstruction


Lecture 61 - Haar wavelet and link to filter banks


Lecture 62 - Demo on wavelet decomposition


Lecture 63 - Problem on circular convolution


Lecture 64 - Time frequency localization


Lecture 65 - Basic analysis: Pointwise and uniform continuity of functions


Lecture 66 - Basic Analysis : Convergence of sequence of functions


Lecture 67 - Fourier series and notions of convergence


Lecture 68 - Convergence of Fourier series at a point of continuity


Lecture 69 - Convergence of Fourier series for piecewise differentiable periodic functions


Lecture 70 - Uniform convergence of Fourier series of piecewise smooth periodic function


Lecture 71 - Convergence in norm of Fourier series


Lecture 72 - Convergence of Fourier series for all square integrable periodic functions


Lecture 73 - Problem on limits of integration of periodic functions


Lecture 74 - Matrix Calculus


Lecture 75 - KL transform


Lecture 76 - Applications of KL transform


Lecture 77 - Demo on KL Transform


Lecture 78 - Live Session


Lecture 79 - Live Session 2