Dual non-negative rational symbols with arbitrary approximation order. (English) Zbl 1069.65151
The construction of dual filters with a prescribed approximation order is considered. Specially, when the primer filter is nonnegative, the authors give a method to construct a nonnegative dual with rational symbol.
Reviewer: Chengshu Wang (Denver)
MSC:
| 65T60 | Numerical methods for wavelets |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
dual filters; rational symbols; non-negative symbol; Bézout identity; wavelets in signal processing.References:
| [1] | Cavaretta, A. S.; Dahmen, W.; Micchelli, C. A., Stationary subdivision, Mem. Amer. Math. Soc, 93, 453 (1991) · Zbl 0741.41009 |
| [2] | Cotronei, M.; Lo Cascio, M. L.; Sauer, T., A class of biorthogonal refinable functions, (Spitaleri, R. M.; Pistella, F., Proceedings of MASCOT02. Proceedings of MASCOT02, IMACS Series in Comput. Appl. Math, vol. 7 (2003), IMACS: IMACS New Brunswick, NJ), 83-90 |
| [3] | Khriji, L.; Gabbouj, M., Vector median rational hybrid filters for multichannel image processing, IEEE Signal Process. Lett, 14, 186-190 (1999) |
| [4] | Gori, L.; Pitolli, F., Multiresolution analysis based on certain compactly supported refinable functions, (Approximation and Optimization, Proc. ICAOR, Cluj-Napoca, Romania (1996)), 81-90 · Zbl 0883.65120 |
| [5] | Jia, R. Q.; Micchelli, C. A., On the linear independence for integer translates of a finite number of functions, Proc. Edinburgh Math. Soc, 36, 69-85 (1992) · Zbl 0790.41016 |
| [6] | Lawton, W. M.; Micchelli, C. A., Construction of conjugate quadrature filters having specified zeros, Numer. Algorithms, 14, 383-399 (1997) · Zbl 0902.65008 |
| [7] | Lawton, W. M.; Micchelli, C. A., Bézout identities with inequality constraints, Vietnam J. Math, 28, 1-29 (2000) · Zbl 0971.65124 |
| [8] | Mallat, S., A Wavelet Tour of Signal Processing (1999), Academic Press: Academic Press New York · Zbl 0998.94510 |
| [9] | Strang, G.; Nguyen, X., Wavelets and Filter Banks (1996), Wellesley-Cambridge Press: Wellesley-Cambridge Press Wellesley, MA · Zbl 1254.94002 |
| [10] | Sweldens, W., The lifting scheme: A custom-design construction of biorthogonal wavelets, ACHA, 3, 186-200 (1996) · Zbl 0874.65104 |
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