Biorthogonal M-channel compactly supported wavelets

Constructive Approximation

Volumn 16, Issue 2, 2000, Pages 283-311

  Soardi, P M ^a  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

Bernstein polynomials; Biorthogonal wavelets; Dual filters; Subband coding

Indexed keywords

EID: 0034340217     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003659910012     Document Type: Article

References (28)

1. N. BI, X. DAI, Q. SUN (1999): Construction of compactly supported M-band wavelets. Appl. Comput. Harmonic Anal., 6:113-131.
2. N. BI, LOKENATH DEBNATH, Q. SUN (1998): Asymptotic behaviour of M-band scaling functions of Daubechies type. Z. Anal. Anwendungen., 17:813-830.
3. L. BRANDOLESE (1997): Condizioni di Cohen, filtri di Bernstein e ondine con fattore di dilatazione p. Tesi, Universitá di Milano.
4. C. S. BURRUS, R. A. GOPINAH, H. GUO (1998): Wavelets and Wavelet Transforms. Upper Saddle River: Prentice Hall.
5. H. CAGLAR, N. AKANSU (1993): A generalized parametric PR-QF design technique based on Bernstein polynomial approximation. IEEE Trans. Signal Process., 41:2314-2321. London: Chapman & Hall, 1995.
6. A. COHEN (1990): Construction de bases d'ondelettes α-Hölderiennes. Rev. Mat. Iberoamericana, 6:91-108.
7. A. COHEN, J. P. CONZE (1992): Régularité des bases d'ondelettes et mesures ergodiques. Rev. Mat. Iberaoamericana, 8:351-365.
8. A. COHEN, I. DAUBECHIES, J. C. FEAUVEAU (1992): Biorthogonal bases of compactly supported wavelets. Comm. Pure Appl. Math., 44:485-560.
9. A. COHEN, R. D. RYAN (1995): Wavelets and Multiscale Signal Processing. London: Chapman & Hall.
10. A. COHEN, J. M. SCHLENKER (1993): Compactly supported bidimensional wavelet base with hexagonal symmetry. Constr. Approx., 9:209-236.
11. C. K. CHUI (1992): An Introduction to Wavelets. Boston: Academic Press.
12. C. K. CHUI, JIAN-AO LIAN (1995): Construction of compactly supported symmetric and antisymmetric orthonormal wavelets with scale = 3. Appl. Comput. Harmonic Anal., 2:21-51.
13. I. DAUBECHIES (1988): Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math., 41:909-996.
14. I. DAUBECHIES (1992): Ten Lectures on Wavelets. CBMS-NSF Series in Applied Mathematics, vol. 61. Philadelphia: SIAM.
15. P. N. HELLER (1995): Rank M wavelets with N vanishing moments. SIAM J. Matrix Appl., 16:502-519.
16. P. N. HELLER, R. O. WELLS (1996): Sobolev regularity for rank M wavelets. CML technical report, Rice University.
17. E. HERNANDEZ, G. WEISS (1996): A First Course on Wavelets. New York: CRC Press.
18. P. G. LEMARIÉ-RIEUSSET (1994): Polynomes de Bernstein en théorie des ondelettes. C. R. Acad. Sci. Paris Sér. I, 319:21-21.
19. P. G. LEMARIÉ-RIEUSSET (1995): Fonctions d'échelle interpolantes, polynomes de Bernstein et ondelettes non stationnaires. Preprint.
20. G. G. LORENTZ (1986): Bernstein Polynomials. New York: Chelsea.
21. X. SHI, Q. SUN (1997): A class of M-dilation scaling functions with regularity growing proportionally to filter support width. Proc. Amer. Math. Soc., 126:3501-3506.
22. P. M. SOARDI (1998): Hölder regularity of compact supported p-wavelets: p = 3, 4, 5. Constr. Approx., 14:387-399.
23. Q. SUN (1999): Sobolev index estimate and asymptotic regularity of M-band Daubechies scaling functions. Const. Approx., 15:441-465.
24. M. VETTERLI (1989): Perfect reconstruction FIR filter banks: Some properties and factorization. IEEE Trans. Acoust. Speech Signal Process., 37:1057-1071.
25. M. VETTERLI, J. KOVACEVIC (1995): Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice Hall.
26. H. VOLKMER (1992): On the regularity of wavelets. IEEE Trans. Inform. Theory, 38:872-876.
27. G. V. WELLAND, M. LUNDBERG (1993): Construction of compact p-wavelets. Constr. Approx., 9:347-370.
28. R. M. YOUNG (1980): An Introduction to Nonharmonic Fourier Series. New York: Academic Press.