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