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Course Co-ordinated by :
IISc Bangalore
Course Available from :
22-December-2017
NPTEL
Electrical Engineering
NOC:Mathematical Methods and Techniques in Signal Processing (Video)
Introduction to signal processing
Modules / Lectures
Introduction to Signal Processing, State Space Representation and Vector Spaces - I
Introduction to signal processing
Basics of signals and systems
Linear time-invariant systems
Modes in a linear system
Introduction to state space representation
State space representation
Non-uniqueness of state space representation
Introduction to vector space
Vector Spaces - II
Linear independence and spanning set
Unique representation theorem
Basis and cardinality of basis
Norms and inner product spaces
Inner products and induced norm
Cauchy Schwartz inequality
Orthonormality
Problem on sum of subspaces
Vector Spaces - III and Signal Geometry
Linear independence of orthogonal vectors
Hilbert space and linear transformation
Gram Schmidt orthonormalization
Linear approximation of signal space
Gram Schmidt orthogonalization of signals
Problem on orthogonal complement
Problem on signal geometry (4-QAM)
Probability and Random Processes
Basics of probability and random variables
Mean and variance of a random variable
Introduction to random process
Statistical specification of random processes
Stationarity of random processes
Problem on mean and variance
Problem on MAP Detection
Sampling Theorem and Multirate Systems - I
Fourier transform of dirac comb sequence
Sampling theorem
Basics of multirate systems
Frequency representation of expanders and decimators
Decimation and interpolation filters
Multirate Systems - II
Fractional sampling rate alterations
Digital filter banks
DFT as filter bank
Noble Identities
Polyphase representation
Efficient architectures for interpolation and decimation filters
Problems on simplifying multirate systems using noble identities
Problem on designing synthesis bank filters
Multirate Systems - III
Efficient architecture for fractional decimator
Multistage filter design
Two-channel filter banks
Amplitude and phase distortion in signals
Multirate Systems - IV
Polyphase representation of 2-channel filter banks, signal flow graphs and perfect reconstruction
M-channel filter banks
Polyphase representation of M-channel filter bank
Perfect reconstruction of signals
Nyquist and half band filters
Special filter banks for perfect reconstruction
Wavelets - I
Introduction to wavelets
Multiresolution analysis and properties
The Haar wavelet
Structure of subspaces in MRA
Haar decomposition - 1
Haar decomposition - 2
Wavelets - II and Continuity of Functions
Wavelet Reconstruction
Haar wavelet and link to filter banks
Demo on wavelet decomposition
Problem on circular convolution
Time frequency localization
Basic analysis: Pointwise and uniform continuity of functions
Fourier Series - I
Basic Analysis : Convergence of sequence of functions
Fourier series and notions of convergence
Convergence of Fourier series at a point of continuity
Convergence of Fourier series for piecewise differentiable periodic functions
Uniform convergence of Fourier series of piecewise smooth periodic function
Fourier Series - II and KL Transform
Convergence in norm of Fourier series
Convergence of Fourier series for all square integrable periodic functions
Problem on limits of integration of periodic functions
Matrix Calculus
KL transform
Applications of KL transform
Demo on KL Transform
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Live Session
Live Session 2
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