Einige Anwendungen der Schnellen Fouriertransformation

Abstract

Many problems in applied and computational analysis require the evaluation of the (discrete) Fourier transform of a sequence of complex numbers with period n. While straightforward evaluation of the transform requires n² multiplications and additions, the fast Fourier transform (FFT) algorithm of Cooley and Tukey achieves the same goal using only n log₂n such operations. Two applications of this algorithm are indicated: a) The Theodorsen method in numerical conformai mapping, where using FFT one iteration costs only O(nlog₂n) operations in place of the O(n²) operations required by the Wittich method; b) computations with formal power series, where using FFT the first n coefficients of products, quotients, and square roots can be obtained in O(n log₂n) operations.