Geodesic
Synthesis of the parameters of multi-dimensional multi-rate systems. Multidimensional fractional delay filters
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 219-238 
M. K. Tchobanou. Synthesis of the parameters of multi-dimensional multi-rate systems. Multidimensional fractional delay filters. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 2, pp. 219-238. http://geodesic.mathdoc.fr/item/SJVM_2008_11_2_a7/
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     title = {Synthesis of the parameters of multi-dimensional multi-rate systems. {Multidimensional} fractional delay filters},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of multi-dimensional multi-rate systems design by application of a lifting technique is considered. In order to solve it, it is proposed to apply the design method of multidimensional digital filters with a fractional delay. A symmetric structure is given for $\tau=(1/2,1/2)$, as well as a new structure based on application of the multidimensional Taylor series. The impulse and the frequency responses are given for the filters with a fractional space delay, their $L_2$ norm being found.

[1] Rabiner L., Gould B., Teoriya i primenenie tsifrovoi obrabotki signalov, Mir, M., 1978

[2] Chobanu M. K., “Mnogomernye mnogoskorostnye sistemy i mnogomernye veivlet funktsii. Chast I. Teoriya”, Vestnik MEI, 2003, no. 2, 75–82

[3] Chobanu M. K., “Sintez osnovnykh elementov mnogomernykh mnogoskorostnykh sistem. Chast I. Nerazdelimye matritsy detsimatsii”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd.-nie — Novosibirsk, 11:1 (2008), 95–113

[4] Chobanu M. K., Batluk A. V., “Issledovanie primeneniya bankov filtrov dlya szhatiya izobrazhenii”, Tsifrovaya obrabotka signalov, 2005, no. 4, 29–40

[5] Chobanu M. K., Karakazyan S. A., “Trekhkanalnye mnogoskorostnye sistemy”, Vestnik Sankt-Peterburgskogo universiteta, seriya 10: Prikladnaya matematika, informatika, protsessy upravleniya, 2007, no. 1, 66–75 | Zbl

[6] Chobanu M. K., Maksimenko I. E., “Sintez dvukhkanalnykh mnogomernykh veivletov i ikh primenenie dlya szhatiya izobrazhenii”, Vestnik MEI, 2006, no. 2, 88–96

[7] Bruekers F., van den Enden A., “New networks for perfect inversion and perfect reconstruction”, IEEE J. on Sel. Areas in Commun., 10:1 (1992), 130–137

[8] Croisier A., Esteban D., Galaud C., “Perfect channel splitting by use of interpolation/decimation/tree decomposition techniques”, Int. Conf. Inform. Sci. Syst. — Greece, 1976, 443–446

[9] Deslauriers G., Dubuc S., Fractals, dimensions non entiéres et applications, Masson, Paris, 1987, 44–55 | MR

[10] de Boor C., Ron A., “On multivariate polynomial interpolation”, Constr. Approxim., 6 (1990), 287–302 | DOI | MR | Zbl

[11] de Boor C., Ron A., “Computational aspects of polynomial interpolation in several variables”, Math. Comp., 58 (1992), 705–727 | DOI | MR | Zbl

[12] Hui J., Riemenschneider S. D., Shen Z., “Multivariate compactly supported fundamental refinable functions, duals and biorthogonal wavelets”, Studies in Applied Mathematics, 102 (1999), 173–204 | DOI | MR | Zbl

[13] Kovačević J., Sweldens W., “Wavelet families of increasing order in arbitrary dimensions”, IEEE Trans. Image Proc., 9:3 (2000), 480–496 | DOI | Zbl

[14] Mitra S., Digital Signal Processing: A Computer-Based Approach, 3 edition, UCSB, Mc Graw Hill, 2006

[15] Riemenschneider S. D., Shen Z., “Construction of compactly supported biorthogonal wavelets II”, Wavelet Applications Signal and Image Processing, VII, Proc. of SPIE, 3813, eds. by M. Unser, A. Aldroubi, and A. Laine, 1999, 264–272

[16] Sweldens W., “The lifting scheme: A construction of second generation wavelets”, SIAM J. on Math. Anal., 29:2 (1998), 511–546 | DOI | MR | Zbl

[17] Sweldens W., Piessens R., “Quadrature formulae and asymptotic error expansionsfor wavelet approximations of smooth functions”, SIAM J. Numer. Anal., 31:4 (1994), 1240–1264 | DOI | MR | Zbl

[18] Tchobanou M., “Design of multidimensional multirate systems and orthogonal and biorthogonal wavelets”, Avtomatizatsiya, upravlenie i informatsionnye tekhnologii (ACIT-2005), Tr. 2-i Mezhdunar. konf., Akademgorodok, Novosibirsk, 2005, 262–267 (in English)

[19] Tekalp A., Digital Video Processing, Prentice Hall, London, 1995

[20] Vaidyanathan P. P., Multirate Systems and Filter Banks, Prentice Hall, Englewood Cliffs, 1993 | Zbl

[21] Vetterli M., Herley C., “Wavelets and filter banks: Theory and design”, IEEE Trans. Acoust., Speech, and Signal Proc., 40:9 (1992), 207–223

[22] Woods J. W., Subband Image Coding, Kluwer Academic Publishers, Norwell, MA, USA, 1991 | Zbl