Lecture 1. Introduction
Lecture 2. Origin of Wavelets
Lecture 3. Haar Wavelet
Lecture 1. Dyadic Wavelet
Lecture 2. Dilates and Translates of Haar Wavelets
Lecture 3.L2 Norm of a Function
Lecture 1.Piecewise Constant Representation of a Function
Lecture 2.Ladder of Subspaces
Lecture 3.Scaling Function for Haar Wavelet Demo:
Demonstration: Piecewise constant approximation of functions
Lecture 1. Vector Representation of Sequences
Lecture 2. Properties of Norm
Lecture 3. Parseval's Theorem
Lecture 1. Equivalence of sequences and functions
Lecture 2. Angle between Functions & their Decomposition
Demo: Additional Information on Direct-Sum
Lecture 1.Introduction to filter banks
Lecture 2.Haar Analysis Filter Bank in Z-domain
Lecture 3.Haar Synthesis Filter Bank in Z-domain.
Lecture 1.Moving from Z-domain to frequency domain
Lecture 2.Frequency Response of Haar Analysis Low pass Filter bank
Lecture 3.Frequency Response of Haar Analysis High pass Filter bank
Lecture 1.Ideal two-band filter bank
Lecture 2.Disqualification of Ideal filter bank
Lecture 3.Realizable two-band filter bank
Demo: Demonstration: DWT of images
Lecture 1.Relating Fourier transform of scaling function to filter bank
Lecture 2.Fourier transform of scaling function
Lecture 3.Construction of scaling and wavelet functions from filter bank
Demo: Demonstration: Constructing scaling and wavelet functions.
Lecture 1.Introduction to upsampling and down sampling as Multirate operations
Lecture 2.Up sampling by a general factor M- a Z-domain analysis.
Lecture 3.Down sampling by a general factor M- a Z-domain analysis.
Lecture 1.Z domain analysis of 2 channel filter bank.
Lecture 2.Effect of X (-Z) in time domain and aliasing.
Lecture 3.Consequences of aliasing and simple approach to avoid it
Lecture 1.Revisiting aliasing and the Idea of perfect reconstruction
Lecture 2.Applying perfect reconstruction and alias cancellation on Haar MRA
Lecture 3.Introduction to Daubechies family of MRA.
Lecture 1.Power Complementarity of low pass filter
Lecture 2.Applying perfect reconstruction condition to obtain filter coefficient
Lecture 1.Effect of minimum phase requirement on filter coefficients
Lecture 2.Building compactly supported scaling functions
Lecture 3.Second member of Daubechies family.
Lecture 1.Fourier transform analysis of Haar scaling and Wavelet functions
Lecture 2.Revisiting Fourier Transform and Parseval's theorem
Lecture 3.Transform Analysis of Haar Wavelet function
Lecture 1.Nature of Haar scaling and Wavelet functions in frequency domain
Lecture 2.The Idea of Time-Frequency Resolution.
Lecture 3.Some thoughts on Ideal time- frequency domain behavior
Lecture 1.Defining Probability Density function
Lecture 2.Defining Mean, Variance and “containment in a given domain”
Lecture 3.Example: Haar Scaling function
Lecture 4.Variance from a slightly different perspective
Lecture 1.Signal transformations: effect on mean and variance
Lecture 2.Time-Bandwidth product and its properties.
Lecture 3.Simplification of Time-Bandwidth formulae
Lecture 1. Introduction
Lecture 2.Evaluation of Time-Bandwidth product
Lecture 3.Optimal function in the sense of Time-Bandwidth product
Lecture 1.Discontent with the “Optimal function”.
Lecture 2.Journey from infinite to finite Time-Bandwidth product of Haar scaling function
Lecture 3.More insights about Time-Bandwidth product
Lecture 4.Time-frequency plane
Lecture 5.Tiling the Time-frequency plane
Lecture 1.STFT: Conditions for valid windows
Lecture 2.STFT: Time domain and frequency domain formulations.
Lecture 3.STFT: Duality in the interpretations
Lecture 4.Continuous Wavelet Transform (CWT)
Conclusive Remarks and Future Prospects
1. Michael W. Frazier, "An Introduction to Wavelets through Linear Algebra”, Springer, 1999.
2. Stephane Mallat, "A Wavelet Tour of Signal Processing", Academic Press, Elsevier, 1998, 1999, Second Edition.
3. http://nptel.ac.in/courses/117101001/: The lecture series on Wavelets and Multirate Digital Signal Processing created by Prof. Vikram M. Gadre in NPTEL.
4. Barbara Burke Hubbard, "The World according to Wavelets - A Story of a Mathematical Technique in the making", Second edition, Universities Press (Private) India Limited 2003.
5. P.P. Vaidyanathan, "Multirate Systems and Filter Banks", Pearson Education, Low Price Edition.