NOC:Fundamentals of Wavelets, Filter Banks and Time Frequency Analysis

Lecture 1 - Module 1 - Lecture 1 - Introduction

Lecture 2 - Module 1 - Lecture 2 - Origin of Wavelets

Lecture 3 - Module 1 - Lecture 3 - Haar Wavelet

Lecture 4 - Module 2 - Lecture 1 - Dyadic Wavelet

Lecture 5 - Module 2 - Lecture 2 - Dilates and Translates of Haar Wavelets

Lecture 6 - Module 2 - Lecture 3 - L2 Norm of a Function

Lecture 7 - Module 3 - Lecture 1 - Piecewise Constant Representation of a Function

Lecture 8 - Module 3 - Lecture 2 - Ladder of Subspaces

Lecture 9 - Module 3 - Lecture 3 - Scaling Function for Haar Wavelet Demo

Lecture 10 - Demonstration 1: Piecewise constant approximation of functions

Lecture 11 - Module 4 - Lecture 1 - Vector Representation of Sequences

Lecture 12 - Module 4 - Lecture 2 - Properties of Norm

Lecture 13 - Module 4 - Lecture 3 - Parseval's Theorem

Lecture 14 - Module 5 - Lecture 1 - Equivalence of sequences and functions

Lecture 15 - Module 5 - Lecture 2 - Angle between Functions and their Decomposition

Lecture 16 - Demonstration 2: Additional Information on Direct-Sum

Lecture 17 - Module 6 - Lecture 1 - Introduction to filter banks

Lecture 18 - Module 6 - Lecture 2 - Haar Analysis Filter Bank in Z-domain

Lecture 19 - Module 6 - Lecture 3 - Haar Synthesis Filter Bank in Z-domain

Lecture 20 - Module 7 - Lecture 1 - Moving from Z-domain to frequency domain

Lecture 21 - Module 7 - Lecture 2 - Frequency Response of Haar Analysis Low pass Filter bank

Lecture 22 - Module 7 - Lecture 3 - Frequency Response of Haar Analysis High pass Filter bank

Lecture 23 - Module 8 - Lecture 1 - Ideal two-band filter bank

Lecture 24 - Module 8 - Lecture 2 - Disqualification of Ideal filter bank

Lecture 25 - Module 8 - Lecture 3 - Realizable two-band filter bank

Lecture 26 - Demonstration 3: Demonstration: DWT of images

Lecture 27 - Module 9 - Lecture 1 - Relating Fourier transform of scaling function to filter bank

Lecture 28 - Module 9 - Lecture 2 - Fourier transform of scaling function

Lecture 29 - Module 9 - Lecture 3 - Construction of scaling and wavelet functions from filter bank

Lecture 30 - Demonstration 4: Demonstration: Constructing scaling and wavelet functions

Lecture 31 - Module 10 - Lecture 1 - Introduction to upsampling and down sampling as Multirate operations

Lecture 32 - Module 10 - Lecture 2 - Up sampling by a general factor M- a Z-domain analysis.

Lecture 33 - Module 10 - Lecture 3 - Down sampling by a general factor M- a Z-domain analysis

Lecture 34 - Module 11 - Lecture 1 - Z domain analysis of 2 channel filter bank.

Lecture 35 - Module 11 - Lecture 2 - Effect of X (-Z) in time domain and aliasing

Lecture 36 - Module 11 - Lecture 3 - Consequences of aliasing and simple approach to avoid it

Lecture 37 - Module 12 - Lecture 1 - Revisiting aliasing and the Idea of perfect reconstruction

Lecture 38 - Module 12 - Lecture 2 - Applying perfect reconstruction and alias cancellation on Haar MRA

Lecture 39 - Module 12 - Lecture 3 - Introduction to Daubechies family of MRA

Lecture 40 - Module 13 - Lecture 1 - Power Complementarity of low pass filter

Lecture 41 - Module 13 - Lecture 2 - Applying perfect reconstruction condition to obtain filter coefficient

Lecture 42 - Module 14 - Lecture 1 - Effect of minimum phase requirement on filter coefficients

Lecture 43 - Module 14 - Lecture 2 - Building compactly supported scaling functions

Lecture 44 - Module 14 - Lecture 3 - Second member of Daubechies family

Lecture 45 - Module 15 - Lecture 1 - Fourier transform analysis of Haar scaling and Wavelet functions

Lecture 46 - Module 15 - Lecture 2 - Revisiting Fourier Transform and Parseval's theorem

Lecture 47 - Module 15 - Lecture 3 - Transform Analysis of Haar Wavelet function

Lecture 48 - Module 16 - Lecture 1 - Nature of Haar scaling and Wavelet functions in frequency domain

Lecture 49 - Module 16 - Lecture 2 - The Idea of Time-Frequency Resolution

Lecture 50 - Module 16 - Lecture 3 - Some thoughts on Ideal time- frequency domain behavior

Lecture 51 - Module 17 - Lecture 1 - Defining Probability Density function

Lecture 52 - Module 17 - Lecture 2 - Defining Mean, Variance and “containment in a given domain”

Lecture 53 - Module 17 - Lecture 3 - Example: Haar Scaling function

Lecture 54 - Module 17 - Lecture 4 - Variance from a slightly different perspective

Lecture 55 - Module 18 - Lecture 1 - Signal transformations: effect on mean and variance

Lecture 56 - Module 18 - Lecture 2 - Time-Bandwidth product and its properties

Lecture 57 - Module 18 - Lecture 3 - Simplification of Time-Bandwidth formulae

Lecture 58 - Module 19 - Lecture 1 - Introduction

Lecture 59 - Module 19 - Lecture 2 - Evaluation of Time-Bandwidth product

Lecture 60 - Module 19 - Lecture 3 - Optimal function in the sense of Time-Bandwidth product

Lecture 61 - Module 20 - Lecture 1 - Discontent with the “Optimal function”.

Lecture 62 - Module 20 - Lecture 2 - Journey from infinite to finite Time-Bandwidth product of Haar scaling function

Lecture 63 - Module 20 - Lecture 3 - More insights about Time-Bandwidth product

Lecture 64 - Module 20 - Lecture 4 - Time-frequency plane

Lecture 65 - Module 20 - Lecture 5 - Tiling the Time-frequency plane

Lecture 66 - Module 21 - Lecture 1 - STFT: Conditions for valid windows

Lecture 67 - Module 21 - Lecture 2 - STFT: Time domain and frequency domain formulations

Lecture 68 - Module 21 - Lecture 3 - STFT: Duality in the interpretations

Lecture 69 - Module 21 - Lecture 4 - Continuous Wavelet Transform (CWT)

Lecture 70 - Demonstration 5

Lecture 71 - Student’s Presentation