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September 25, 2023

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Description

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)

Course Curriculum

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

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