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Wavelets and filter banks: theory and design
Open accessAbstract
The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient conditions for the existence of a complementary high-pass filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular filter banks, which generate biorthogonal continuous wavelet bases with symmetries.>
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Cites
The wavelet transform, time-frequency localization and signal analysis
Daubechies, I. (1990) · IEEE Transactions on Information Theory · doi:10.1109/18.57199 · Cited by 6,483
The Laplacian pyramid as a compact image code
Burt, P., & Adelson, E. (1983) · IEEE Transactions on Communications · doi:10.1109/tcom.1983.1095851 · Cited by 6,077
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Metadata
- Authors
- Vetterli, M., & Herley, C.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 1992
- Volume
- 40
- Issue
- 9
- Pages
- 2207-2232
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2149072817
- Cited by
- 1,690
- References
- 2
- FWCI
- 88.08
- Type
- journal article
- Language
- en
- Open access
- green
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