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Vector representation of sequences
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Classroom Contents
Foundations of Wavelets and Multirate Digital Signal Processing
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- 1 Introduction
- 2 Haar wavelet
- 3 Origin of wavelets
- 4 Dyadic wavelet
- 5 Dilates and translates of Haar wavelet
- 6 L2 norm of a function
- 7 Piecewise constant representation of a function
- 8 Ladder of subspaces
- 9 Scaling function of Haar wavelet
- 10 Demonstration: Piecewise constant approximation of functions
- 11 Vector representation of sequences
- 12 Properties of norm
- 13 Parsevals theorem
- 14 Equivalence of functions & sequences
- 15 Angle between Functions & their Decomposition
- 16 Additional Information on Direct-Sum
- 17 Introduction to filter banks
- 18 Haar Analysis filter bank in Z-domain
- 19 Haar Synthesis filter bank in Z-domain
- 20 Moving from Z-domain to frequency domain
- 21 Frequency Response of Haar Analysis Low pass Filter bank
- 22 Frequency Response of Haar Analysis High pass Filter bank
- 23 Disqualification of Ideal Filter bank
- 24 Ideal Two-band Filter bank
- 25 Realizable Two-band Filter bank
- 26 Demonstration: DWT of images
- 27 Relating Fourier transform of scaling function to filter bank
- 28 Fourier transform of scaling function
- 29 Construction of scaling and wavelet functions from filter bank
- 30 Demonstration: Constructing scaling and wavelet functions.
- 31 Conclusive Remarks and Future Prospects
