lecture09: Wavelets and multi-resolution analysis
This lecture introduces wavelets.
Topics covered
- Limitations of the STFT
- Cutting up the time-frequency space
- Scaling property of FT
- Heisenberg's Uncertainty Principle
- Uncertainty Principle
- Gabor function
- Cutting up the time-frequency space
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- Gabor transform
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- Wigner-Ville Distribution
- An alternative
- Wavelets
- Definition: Atoms
- Continuous wavelet transform
- Wavelets
- Wavelet Example
- Example wavelet transform
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- Admissibility
- Wavelet Basis
- Dyadic grid
- Wavelet Partition
- Cutting up the time-frequency space
- Wavelet transforms
- Scalogram
- Time-Frequency Measurement
- Time-Frequency resolution
- MultiResolution Analysis
- Approximation
- Projection
- Approximation
- MultiResolution Approximation (MRA)
- MRA example
- MRA examples
- MRA and scaling functions
- The Approximation
- Relationship to wavelets
- Example: Haar wavelets
- Haar wavelets
- Haar wavelets: freq. representation
- Subband coding
- MRA and wavelets
- Successive decompositions
- MRA and wavelets
- The Scaling Function
- Wavelet Properties
- Applications
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- Conjugate mirror filters
- Riesz basis