Learn · Fundamentals of Wavelets, Filter Banks and Time Frequency Analysis
Lecture 43 of 71Week 5
Module 14: Lecture 2: Building compactly supported scaling functions
Prof. V. M. Gadre · IIT Bombay
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- Fundamentals of Wavelets, Filter Banks and Time Frequency Analysis, IIT Bombay (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- 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 of Haar scaling function
- 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
- Student’s Presentation