Filter Functions with Exponential Convergence Order

✍ Scribed by Robert Denk

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 253 KB
• Volume: 169
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19941690110

✦ Synopsis

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 ((ζ^2^ − 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 (−x^σ^)) with σ arbitrary close to 1.