eprintid: 9450 rev_number: 13 eprint_status: archive userid: 1903 dir: disk0/00/00/94/50 datestamp: 2011-11-10 11:09:43 lastmod: 2016-04-20 17:52:01 status_changed: 2011-11-10 11:09:43 type: article metadata_visibility: show item_issues_count: 0 creators_name: Perez Villalon, Gerardo title: Quasi-interpolation by means of filter-banks ispublished: pub subjects: matematicas abstract: We consider the problem of approximating a regular function f(t) from its samples, f(nT), taken in a uniform grid. Quasi-interpolation schemes approximate f(t) with a dilated version of a linear combination of shifted versions of a kernel ??(t), specifically fapprox T(t) = ??af[n]??(t/T - n), in a way that the polynomials of degree at most L-1 are recovered exactly. These approximation schemes give order L, i.e., the error is O(TL) where T is the sampling period. Recently, quasi-interpolation schemes using a discrete prefiltering of the samples f(nT) to obtain the coefficients af[n], have been proposed. They provide tight approximation with a low computational cost. In this work, we generalize considering rational filter banks to prefilter the samples, instead of a simple filter. This generalization provides a greater flexibility in the design of the approximation scheme. The upsampling and downsampling ratio r of the rational filter bank plays a significant role. When r = 1, the scheme has similar characteristics to those related to a simple filter. Approximation schemes corresponding to smaller ratios give less approximation quality, but, in return, they have less computational cost and involve less storage load in the system date: 2010-02 date_type: published publisher: IEEE official_url: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5339141&tag=1 id_number: 10.1109/TSP.2009.2037063 full_text_status: public publication: IEEE Transactions on Signal Processing volume: 58 number: 3 pagerange: 1628-1637 institution: E_Telecomunicacion department: Matematica_Aplicada6 refereed: TRUE issn: 1053-587X rights: by-nc-nd citation: Perez Villalon, Gerardo (2010). Quasi-interpolation by means of filter-banks. "IEEE Transactions on Signal Processing", v. 58 (n. 3); pp. 1628-1637. ISSN 1053-587X. https://doi.org/10.1109/TSP.2009.2037063 . document_url: https://oa.upm.es/9450/2/INVE_MEM_2010_88030.pdf