2023-03-24T05:13:42Z
https://oa.upm.es/cgi/oai2
oai:oa.upm.es:9450
2016-04-20T17:52:01Z
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Quasi-interpolation by means of filter-banks
Perez Villalon, Gerardo
Mathematics
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
E.U.I.T. Telecomunicación (UPM)
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
2010-02
info:eu-repo/semantics/article
Article
IEEE Transactions on Signal Processing, ISSN 1053-587X, 2010-02, Vol. 58, No. 3
PeerReviewed
application/pdf
eng
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5339141&tag=1
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1109/TSP.2009.2037063
https://oa.upm.es/9450/