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Advanced Digital Signal Processing: Multirate and Wavelets

Advanced Digital Signal Processing: Multirate and Wavelets. Instructor: Prof. Vikram M. Gadre, Department of Electrical Engineering, IIT Bombay. This course discusses topics in wavelets and multirate digital signal processing. The aim of this course is to introduce the idea of wavelets, and the related notions of time-frequency analysis, of time-scale analysis, and to describe the manner in which technical developments related to wavelets have led to numerous applications. A discussion on multirate filter banks will also form an important part of the course. The relation between wavelets and multirate systems will be brought out; to illustrate how wavelets may actually be realized in practice. (from nptel.ac.in)

Lecture 48 - Towards Selecting Wavelets through Vanishing Moments


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Lecture 01 - Introduction
Lecture 02 - The Haar Wavelet
Lecture 03 - The Haar Multiresolution Analysis
Lecture 04 - Wavelets and Multirate Digital Signal Processing
Lecture 05 - Equivalence - Functions and Sequences
Lecture 06 - The Haar Filter Bank
Lecture 07 - Haar Filter Bank Analysis and Synthesis
Lecture 08 - Relating ψ, φ and the Filters
Lecture 09 - Iterating the Filter Bank from ψ, φ
Lecture 10 - Z-Domain Analysis of Multirate Filter Bank
Lecture 11 - Two Channel Filter Bank
Lecture 12 - Perfect Reconstruction - Conjugate Quadrature
Lecture 13 - Conjugate Quadrature Filters - Daubechies Family of MRA
Lecture 14 - Daubechies Filter Banks - Conjugate Quadrature Filters
Lecture 15 - Time and Frequency Joint Perspective
Lecture 16 - Ideal Time Frequency Behaviour
Lecture 17 - The Uncertainty Principle
Lecture 18 - Time Bandwidth Product Uncertainty
Lecture 19 - Evaluating and Bounding σt2 and σω2
Lecture 20 - The Time Frequency Plane and its Tilings
Lecture 21 - Short Time Fourier Transform and Wavelet Transform in General
Lecture 22 - Reconstruction and Admissibility
Lecture 23 - Admissibility in Detail, Discretization of Scale
Lecture 24 - Logarithmic Scale Discretization, Dyadic Discretization
Lecture 25 - The Theorem of (Dyadic) Multiresolution Analysis
Lecture 26 - Proof of the Theorem of (Dyadic) Multiresolution Analysis
Lecture 27 - Introducing Variants of the Multiresolution Analysis Concept
Lecture 28 - JPEG 2000 5/3 Filter Bank and Spline MRA
Lecture 29 - Orthogonal Multiresolution Analysis with Splines
Lecture 30 - Building Piecewise Linear Scaling Function, Wavelet
Lecture 31 - The Wavelet Packet Transform
Lecture 32 - Nobel Identities and the Haar Wave Packet Transform
Lecture 33 - The Lattice Structure for Orthogonal Filter Banks
Lecture 34 - Constructing the Lattice and its Variants
Lecture 35 - The Lifting Structure and Polyphase Matrices
Lecture 36 - The Polyphase Approach - The Modulation Approach
Lecture 37 - Modulation Analysis and the 3-Band Filter Bank Applications
Lecture 38 - The Applications: Data Mining, Face Recognition
Lecture 39 - Proof that a Non-zero Function can not be both Time and Band Limited
Lecture 40 - M-Band Filter Banks and Looking Ahead
Lecture 41 - Tutorial Session I
Lecture 42 - Student Presentation
Lecture 43 - Tutorial on Uncertainty Product
Lecture 44 - Tutorial on Two Band Filter Bank
Lecture 45 - Tutorial - Frequency Domain Analysis of Two Band Filter Bank
Lecture 46 - Zoom In and Zoom Out using Wavelet Transform
Lecture 47 - More Thoughts on Wavelet: Zooming In
Lecture 48 - Towards Selecting Wavelets through Vanishing Moments
Lecture 49 - In Search of Scaling Coefficients
Lecture 50 - Wavelet Applications