Journal ArticleDOI
FFT as Nested Multiplication, with a Twist
Reads0
Chats0
TLDR
A simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.Abstract:
A simple, yet complete and detailed description of the fast Fourier transform for general N is given with the aim of making the underlying idea quite apparent. To help with this didactic goal, a simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.read more
Citations
More filters
Journal ArticleDOI
Self-sorting mixed-radix fast Fourier transforms
Clive Temperton,Clive Temperton +1 more
TL;DR: The implementation of the FFT on vector computers is described, and in the final section it is demonstrated how savings can be achieved in the case of two-dimensional transforms.
Journal ArticleDOI
On arithmetical algorithms over finite fields
TL;DR: An analogue of the fast Fourier transform which efficiently evaluates a polynomial on some of the additive subgroups of F .
Journal ArticleDOI
Analysis of palaeomagnetic time series — Techniques and applications
TL;DR: This review is intended to provide an introduction for the nonspecialist to concepts and techniques which are useful for analysing palaeomagnetic time series, particularly the periodogram and maximum entropy methods.
Journal ArticleDOI
A stochastic roundoff error analysis for the fast Fourier transform
TL;DR: The accuracy of the output of the Fast Fourier Transform is studied by estimating the expectedvalue and the variance of the accompanying linear forms in terms of the expected value and variance ofThe relative roundoff errors for the elementary operations of addition and multiplication.
References
More filters
Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Book
Spectral analysis and its applications
TL;DR: In this paper, Spectral Analysis and its Applications, the authors present a set of applications of spectral analysis and its application in the field of spectroscopy, including the following:
The fast Fourier Transform
TL;DR: A computer algorithm that computes the discrete Fourier transform much faster than other algorithms, is explained and examples and detailed procedures are provided to assist the reader in learning how to use the algorithm.
Journal ArticleDOI
On computing the discrete Fourier transform
TL;DR: New algorithms for computing the Discrete Fourier Transform of n points are described, which use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions.
Related Papers (5)
Vector coding algorithms for multidimensional discrete Fourier transform
Zhaodou Chen,Lijing Zhang +1 more