NOC:Mathematical Methods and Techniques in Signal Processing

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Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Shayan Srinivasa Garani

NPTEL Co-ordinating Institute : IISc Bangalore

NPTEL Lecture Count : 79

NPTEL Course Size : 19 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)


Lecture Titles:

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

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