Module 1: Lecture 1: Introduction

Module 1: Lecture 2: Origin of Wavelets

Module 1: Lecture 3: Haar Wavelet

Module 2: Lecture 1: Dyadic Wavelet

Module 2: Lecture 2: Dilates and Translates of Haar Wavelets

Module 2: Lecture 3: L2 Norm of a Function

Module 3: Lecture 1: Piecewise Constant Representation of a Function?

Module 3: Lecture 2: Ladder of Subspaces

Module 3: Lecture 3: Scaling Function for Haar Wavelet Demo

Demonstration 1: Piecewise constant approximation of functions

Module 4: Lecture 1: Vector Representation of Sequences

Module 4: Lecture 2: Properties of Norm?

Module 4: Lecture 3: Parseval's Theorem

Module 5: Lecture 1: Equivalence of sequences and functions?

Module 5: Lecture 2: Angle between Functions & their Decomposition

Demonstration 2: Additional Information on Direct-Sum

Module 6: Lecture 1: Introduction to filter banks

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

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

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

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

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

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

Module 8: Lecture 2: Disqualification of Ideal filter bank

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

Demonstration 3: Demonstration: DWT of images

Module 9: Lecture 1: Relating Fourier transform of scaling function to filter bank?

Module 9: Lecture 2: Fourier transform of scaling function?

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

Demonstration 4: Demonstration: Constructing scaling and wavelet functions

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

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

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

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

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

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

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

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

Module 12: Lecture 3: Introduction to Daubechies family of MRA

Module 13: Lecture 1: Power Complementarity of low pass filter

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

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

Module 14: Lecture 2: Building compactly supported scaling functions

Module 14: Lecture 3: Second member of Daubechies family

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

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

Module 15: Lecture 3: Transform Analysis of Haar Wavelet function

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

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

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

Module 17: Lecture 1: Defining Probability Density function

Module 17: Lecture 2: Defining Mean, Variance and containment in a given domain

Module 17: Lecture 3: Example: Haar Scaling function

Module 17: Lecture 4: Variance from a slightly different perspective

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

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

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

Module 19: Lecture 1: Introduction

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

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

Module 20: Lecture 1: Discontent with the Optimal function

Module 20: Lecture 2: Journey from infinite to finite Time-Bandwidth product?

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

Module 20: Lecture 4: Time-frequency plane

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

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

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

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

Module 21: Lecture 4: Continuous Wavelet Transform (CWT)

Demonstration 5

Students Presentation