Learn · Foundations of Wavelets and Multirate Digital Signal Processing
Lecture 7 of 33Week 2
Piecewise constant representation of a function
Prof. V. M. Gadre · IIT Bombay
Credits and licence
- From
- Foundations of Wavelets and Multirate Digital Signal Processing, IIT Bombay (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Teens profiles and older. How courses are placed
All the lectures
- Introduction
- Origin of wavelets
- Haar wavelet
- Dyadic wavelet
- Dilates and translates of Haar wavelet
- L2 norm of a function
- Piecewise constant representation of a function
- Ladder of subspaces
- Scaling function of Haar wavelet
- Demonstration: Piecewise constant approximation of functions
- Vector representation of sequences
- Properties of norm
- Parsevals theorem
- Equivalence of functions & sequences
- Angle between Functions & their Decomposition
- Additional Information on Direct-Sum
- Introduction to filter banks
- Haar Analysis filter bank in Z-domain
- Haar Synthesis filter bank in Z-domain
- Moving from Z-domain to frequency domain
- Frequency Response of Haar Analysis Low pass Filter bank
- Frequency Response of Haar Analysis High pass Filter bank
- Ideal Two-band Filter bank
- Disqualification of Ideal Filter bank
- Realizable Two-band Filter bank
- Demonstration: DWT of images
- Relating Fourier transform of scaling function to filter bank
- Fourier transform of scaling function
- Construction of scaling and wavelet functions from filter bank
- Demonstration: Constructing scaling and wavelet functions.
- Conclusive Remarks and Future Prospects
- Live Session 20-02-2024
- Live Session 21-02-2025