Filter Functions with Exponential Convergence Order
Robert Denk · Mathematische Nachrichten · 1994
Abstract Oversampled functions can be evaluated using generalized sinc‐series and filter functions connected with these series. A standard filter function is given by exp ((ζ2 − 1)−1). We show that the Fourier transform of this filter posseses the convergence order 0(exp (−√x)), improving an estimation given in [10]. Moreover, we define a family of filter functions with convergence order O(x · exp (−xσ)) with σ arbitrary close to 1.