%0 Journal Article
%@ 1053-587X
%A Perez Villalon, Gerardo
%D 2010
%F upm:9450
%I IEEE
%J IEEE Transactions on Signal Processing
%N 3
%P 1628-1637
%R 10.1109/TSP.2009.2037063
%T Quasi-interpolation by means of filter-banks
%U https://oa.upm.es/9450/
%V 58
%X 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