Filter functions with exponential convergence order
Abstract. Oversampled functions can be evaluated using generalized sinc-series and filter functions connected with these series. First we consider a standard filter defined by terms of the exponential function . We show that the Fourier transform of this filter posseses exponential convergence order where in the exponent the square root of the independent variable appears. This improves an estimate given in a paper of F. Natterer. Moreover, we define a more general family of filter functions with exponential convergence order where now in the exponent the power of the independent variable is arbitrary close to 1.
Math. Nachr. 169 (1994), 107-115.
The paper is available here: pdf