CUDA Fortran for Scientists and Engineers, 2nd Edition

Chapter 11: Applications of the fast Fourier transform

Abstract

This chapter shows some applications of the fast Fourier transform and how to utilize the CUFFT library.

Keywords

Spectral derivative; CUFFT; Convolution; Overlapping of transfers and compute

The Fourier transform is of fundamental importance in several fields, from image processing to computational physics, just to name a few. The discrete Fourier transform (DFT) is an approximation in which discrete samples of a function f in physical space can be transformed into the Fourier coefficients $\hat{f}$ via the relation

${\hat{f}}_k=\frac{1}{N}\sum _{j=0}^{N-1}{e}^{-\frac{2\pi ı}{N}jk}{f}_j.$

This formula can be rewritten as a matrix–vector product ...