Quasi-interpolation by means of filter-banks

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.


Title: Quasi-interpolation by means of filter-banks
  • Perez Villalon, Gerardo
Item Type: Article
Título de Revista/Publicación: IEEE Transactions on Signal Processing
Date: February 2010
Volume: 58
Faculty: E.U.I.T. Telecomunicación (UPM)
Department: Matemática Aplicada a la Ingeniería Técnica de Telecomunicación [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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

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Item ID: 9450
DC Identifier: http://oa.upm.es/9450/
OAI Identifier: oai:oa.upm.es:9450
Deposited by: Memoria Investigacion
Deposited on: 10 Nov 2011 11:09
Last Modified: 20 Apr 2016 17:52
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