A new Fourier transform

A New Fourier Transform

In order to define a geometric Fourier transform, one usually works with either `-adic sheaves in characteristic p > 0 or with D-modules in characteristic 0. If one considers `-adic sheaves on the stack quotient of a vector bundle V by the homothety action of Gm, however, Laumon provides a uniform geometric construction of the Fourier transform in any characteristic. The category of sheaves on ...

A New Fast Discrete Fourier Transform

This paper presents a new fast Discrete Fourier Transform (DFT) algorithm. By rewriting the DFT, a new algorithm is obtained that uses 2 n?2 (3n?13)+4n?2 real multiplications and 2 n?2 (7n? 29) + 6n + 2 real additions for a real data N = 2 n point DFT, comparable to the number of operations in the Split-Radix method, but with slightly fewer multiply and add operations in total. Because of the o...

A Fourier Transform

The harmonic function F exp(j2rvt) plays an important role in science and engineering. It has frequency v and complex amplitude F. Its real part IFIcos(2~vt + arg{F}) is a cosine function with amplitude jF( and phase arg{F}. The variable t usually represents time; the frequency v has units of cycles/s or Hz. The harmonic function is regarded as a building block from which other functions may be...

The Fourier Transform { A

A new numerical Fourier transform in d-dimensions

The classical method of numerically computing Fourier transforms of digitized functions in one or in -dimensions is the so-called discrete Fourier transform (DFT) efficiently implemented as fast Fourier transform (FFT) algorithms. In many cases, the DFT is not an adequate approximation to the continuous Fourier transform, and because the DFT is periodical, spectrum aliasing may occur. The metho...