title: Quasi-interpolation by means of filter-banks
creator: Perez Villalon, Gerardo
subject: Mathematics
description: 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
publisher: E.U.I.T. Telecomunicación (UPM)
rights: https://creativecommons.org/licenses/by-nc-nd/3.0/es/
date: 2010-02
type: info:eu-repo/semantics/article
type: Article
source: IEEE Transactions on Signal Processing, ISSN 1053-587X, 2010-02, Vol. 58, No. 3
type: PeerReviewed
format: application/pdf
language: eng
relation: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5339141&tag=1
rights: info:eu-repo/semantics/openAccess
relation: info:eu-repo/semantics/altIdentifier/doi/10.1109/TSP.2009.2037063
identifier: https://oa.upm.es/9450/