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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 19 - Evaluating and Bounding σ_t² and σ_ω²

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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 σ_t² and σ_ω²

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