Fast Algorithms for Discrete and Continuous Wavelet Transforms

IEEE Transactions on Information Theory

Volumn 38, Issue 2, 1992, Pages 569-586

  Rioul, Olivier ^a   Duhamel, Pierre ^a  

^a ORANGE LABS   (France)

Author keywords

computational complexity; continuous wavelet; Discrete wavelet transform; fast FIR filtering algorithms; fast Fourier transform; octave band filter banks; transform

Indexed keywords

ELECTRIC FILTERS, DIGITAL; INFORMATION THEORY; SIGNAL FILTERING AND PREDICTION;

CONTINUOUS WAVELET TRANSFORMS; DISCRETE WAVELET TRANSFORMS; FAST FIR FILTERING; FAST FOURIER TRANSFORM; OCTAVE-BASED FILTER BANKS;

MATHEMATICAL TRANSFORMATIONS;

EID: 0026745217     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.119724     Document Type: Article

References (34)

1. M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, “Imaging coding using vector quantization in the wavelet transform domain,” in Proc. 1990 IEEE Int. Conf. Acoust., Speech, Signal Processing, Albuquerque, NM, Apr. 3–6, 1990, pp. 2297–2300.
2. J. Bertrand, P. Bertrand, and J. P. Ovarlez, “Discrete Mellin transform for signal analysis,” in Proc. 1990 IEEE Int. Conf. Acoust., Speech, Signal Processing, Albuquerque, NM, Apr. 3–6, 1990, pp. 1603–1606.
3. A. Cohen, I. Daubechies, and J. C. Feauveau, “Biorthogonal bases of compactly supported wavelets,” Tech. Memo. #11217-900529-07, AT&T Bell Labs.; to appear in Comm. Pure Applied Math.
4. I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Comm. in Pure Applied Math., vol. 41, no. 7, pp. 909–996, 1988.
5. I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inform. Theory, vol. 36, pp. 961–1005, Sept. 1990.
6. I. Daubechies and J. C. Lagarias, “Two-scale difference equations I. Existence and global regularity of solutions,” SIAM J. Math. Anal., vol. 22, no. 5, pp. 1388–1410, Sept. 1991.
7. G. Deslauriers and S. Dubuc, “Symmetric iterative interpolation processes,” Constructive Approximation, vol. 5, pp. 49–68, 1989.
8. P. Duhamel, “Implementation of split-radix FFT algorithms for complex, real, and real-symmetric data,” IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-34, pp. 285–295, Apr. 1986.
9. P. Dutilleux, “An implementation of the ‘Algorithme á Trous’ to compute the wavelet transform,” in Wavelets, Time-Frequency Methods and Phase Space, J. M. Combas, A. Grossmann, and Ph. Tchamitchian, Eds. Berlin: Springer, IPTI, 1989, pp. 298–304.
10. G. Evangelista, “Orthogonal wavelet transforms and filter banks,” presented at Proc. 23rd Asilomar Conf., IEEE, Nov. 1989.
11. P. Flandrin, “Some aspects of non-stationary signal processing with emphasis on time-frequency and time-scale methods,” in Wavelets, Time-Frequency Methods and Phase Space, J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Eds. Berlin: Springer, IPTI, 1989, pp. 68–98.
12. R. A. Gopinath and C. S. Burrus, “Efficient computation of the wavelet transforms,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, Albuquerque, NM, Apr. 3–6, 1990, pp. 1599–1601.
13. P. Goupillaud, A. Grossmann, and J. Morlet, “Cycle-octave and related transforms in seismic signal analysis,” Geoexploration, vol. 23, pp. 85–102, 1984/85.
14. A. Grossmann and R. Kronland-Martinet, “Time and scale representations obtained through continuous wavelet transforms,” in Proc. Int. Conf. EUSIPCO’88, Signal Processing IV: Theories and Applications, J. L. Lacoume et al., Eds. New York: Elsevier Science Pub., 1988, pp. 475–482.
15. C. E. Heil and D. F. Walnut, “Continuous and discrete wavelet transforms,” SIAM Rev., vol. 31, no. 4, pp. 628–666, Dec. 1989.
16. C. E. Heil, “Wavelets and frames,” in Signal Processing, Part I: Signal Processing Theory, vol. 22, L. Auslander, T. Kailath, S. Mitter, Eds., Institute for Mathematics and its Applications. New York: Springer, 1990.
17. M. Holschneider, R. Kronland-Martinet, J. Morlet, and Ph. Tchamitchian, “A real-time algorithm for signal analysis withthe help of the wavelet transform,” in Wavelets, Time-Frequency Methods and Phase Space, J. M. Combes, A. Grossmann, and Ph. Tchamitchian, Eds. Berlin: Springer, IPTI, 1989, pp. 286–297.
18. R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artificial Intell., vol. 1, no. 2, 1987. pp. 273–302.
19. S. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674–693, July 1989.
20. S. Mallat, “Multifrequency channel decompositions of images and wavelet models,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 2091–2110, Dec. 1989.
21. S. Mallat and S. Zhong, “Signal characterization from multiscale edges,” in Proc. 10th Int. Conf. Pattern Recogn., Pattern Recogn., Syst. Applica., Los Alamitos, CA, 16–21 June 1990, pp. 891–896.
22. Y. Meyer, Ondelettes et Opérateurs, Tome I. Paris: Herrmann, 1990.
23. Z. J. Mou and P. Duhamel, “Short-length FIR filters and their use in fast nonrecursive filtering,” IEEE Trans. Signal Proc., vol. 39, pp. 1322–1332, June 1991.
24. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms. Berlin: Springer, 1981.
25. T. A. Ramstad and T. Saramaki, “Efficient multirate realization for narrow transition-band FIR filters,” in IEEE 1988 Int. Symp. Cir. and Systems, 1988, pp. 2019–2022.
26. M. J. Shensa, “Affine wavelets: Wedding the Atrous and Mallat algorithms,” to appear in IEEE Trans. Acoust., Speech, Signal Proc.
27. M. J. T. Smith and T. P. Barnwell, “Exact reconstruction for tree-structured subband coders,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 434–441, June 1986.
28. P. P. Vaidyanathan and P.-Q. Hoang, “Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 81–94, Jan. 1988.
29. P. P. Vaidyanathan, “Multirate digital filters, filter banks, polyphase networks, and applications: A tutorial,” Proc. IEEE, vol. 78, pp. 56–93, Jan. 1990.
30. M. Vetterli, “Analyse, Synthése et Complexité de Calcul de Bancs de Filtres Numériques,” Ph.D. thesis, Ecole Polytechique Fédérale de Lausanne, 1986.
31. ―, “Running FIR and IIR filtering using multirate filter banks,” IEEE Trans. Acoust., Speech, Signal Proc., vol. ASSP-36, pp. 730–738, May 1988.
32. M. Vetterli and C. Herley, “Wavelets and filter banks: Relationships and new results,” in Proc. 1990 IEEE Int. Conf. Acoust., Speech, Signal Processing, Albuquerque, NM, Apr. 3–6, 1990, pp. 1723–1726.
33. M. Vetterli and C. Herley, “Wavelets and filter banks: Theory and design,” to appear in IEEE Trans. Acoust., Speech, Signal Processing.
34. J. M. Combes, A. Grossmann, Ph. Tchamitchian, Eds., Wavelets, Time-Frequency Methods and Phase Space, Berlin: Springer, IPTI, 1989.