Wavelets and filter banks: theory and design
作者： M. Vetterli , C. Herley
DOI: 10.1109/78.157221
关键词: Quadrature mirror filter 、 Mathematics 、 Second-generation wavelet transform 、 Lifting scheme 、 Filter design 、 Algorithm 、 Continuous wavelet 、 Arithmetic 、 Filter bank 、 Wavelet 、 Discrete wavelet transform
摘要: The wavelet transform is compared with the more classical short-time Fourier approach to signal analysis. Then relations between wavelets, filter banks, and multiresolution processing are explored. A brief review given of perfect reconstruction which can be used both for computing discrete transform, deriving continuous bases, provided that filters meet a constraint known as regularity. Given low-pass filter, necessary sufficient conditions existence complementary high-pass will permit derived. condition posed Bezout identity, it shown how possible find all higher-degree based on an analogy theory Diophantine equations. An alternative continued fractions also given. These results design highly regular generate biorthogonal bases symmetries. >
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sci-hub.se 参考文章(34)
M. Smith, T. Barnwell, A procedure for designing exact reconstruction filter banks for tree-structured subband coders international conference on acoustics, speech, and signal processing. ,vol. 9, pp. 421- 424 ,(1984) , 10.1109/ICASSP.1984.1172486
A. Grossmann, R. Kronland-Martinet, J. Morlet, Reading and Understanding Continuous Wavelet Transforms inverse problems and theoretical imaging. pp. 2- 20 ,(1990) , 10.1007/978-3-642-75988-8_1
Martin Vetterli, Filter banks allowing perfect reconstruction Signal Processing. ,vol. 10, pp. 219- 244 ,(1986) , 10.1016/0165-1684(86)90101-5
M. Portnoff, Time-frequency representation of digital signals and systems based on short-time Fourier analysis IEEE Transactions on Acoustics, Speech, and Signal Processing. ,vol. 28, pp. 55- 69 ,(1980) , 10.1109/TASSP.1980.1163359
T.Q. Nguyen, P.P. Vaidyanathan, Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters IEEE Transactions on Acoustics, Speech, and Signal Processing. ,vol. 37, pp. 676- 690 ,(1989) , 10.1109/29.17560
P. Goupillaud, A. Grossmann, J. Morlet, Cycle-octave and related transforms in seismic signal analysis Geoexploration. ,vol. 23, pp. 85- 102 ,(1984) , 10.1016/0016-7142(84)90025-5
I. Daubechies, The wavelet transform, time-frequency localization and signal analysis IEEE Transactions on Information Theory. ,vol. 36, pp. 961- 1005 ,(1990) , 10.1109/18.57199
O. Herrmann, On the approximation problem in nonrecursive digital filter design IEEE Transactions on Circuit Theory. ,vol. 18, pp. 411- 413 ,(1971) , 10.1109/TCT.1971.1083275
P.P. Vaidyanathan, P.-Q. Hoang, Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks IEEE Transactions on Acoustics, Speech, and Signal Processing. ,vol. 36, pp. 81- 94 ,(1988) , 10.1109/29.1491
Gilbert Strang, Wavelets and Dilation Equations: A Brief Introduction SIAM Review. ,vol. 31, pp. 614- 627 ,(1989) , 10.1137/1031128