On general transforms hill functions

Abstract

Besides their various numerical applications, the hill functions (β-splines) have been used in a disguised way, for signal analysis, as an efficient filter to be convolved with the usual ideal low pass filter (hill function of order one). This resulted in a self truncating sampling series for a better truncation error bound. For sampling expansions associated with more general integral transforms besides the Fourier transform, the need arises for their associated hill functions in order to improve the convergence of their sampling series. The subject of this paper is to develop new generalized hill functions along with their basic properties, computations, and the application of their transform to the construction of a self-truncating generalized sampling series.

AMS (MOS) 65D07, 65D05, 42A38, 44A15

Additional information

Notes on contributors

A. J. Jerri

M. Z. Nashed