Quasi-interpolation by means of filter-banks

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 fT approx(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, quasiinterpolation 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 ...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Gerardo Pérez-Villalón
• Keywords: Approximation Schemes, Artificial Intelligence, Rational Filter Bank, Simple Filter, TSP 2010