Journal ArticleDOI
Numerical Analysis: A fast fourier transform algorithm for real-valued series
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TLDR
In this article, a new procedure for calculating the complex, discrete Fourier transform of real-valued time series is presented for an example where the number of points in the series is an integral power of two.Abstract:
A new procedure is presented for calculating the complex, discrete Fourier transform of real-valued time series. This procedure is described for an example where the number of points in the series is an integral power of two. This algorithm preserves the order and symmetry of the Cooley-Tukey fast Fourier transform algorithm while effecting the two-to-one reduction in computation and storage which can be achieved when the series is real. Also discussed are hardware and software implementations of the algorithm which perform only (N/4) log2 (N/2) complex multiply and add operations, and which require only N real storage locations in analyzing each N-point record.read more
Citations
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Journal ArticleDOI
The Design and Implementation of FFTW3
Matteo Frigo,Steven G. Johnson +1 more
TL;DR: It is shown that such an approach can yield an implementation of the discrete Fourier transform that is competitive with hand-optimized libraries, and the software structure that makes the current FFTW3 version flexible and adaptive is described.
Journal ArticleDOI
A guided tour of the fast Fourier transform
TL;DR: This article is intended as a primer on the fast Fourier transform, which has revolutionized the digital processing of waveforms and is needed for a whole new range of applications for this classic mathematical device.
Journal ArticleDOI
Real-valued fast Fourier transform algorithms
TL;DR: A new implementation of the real-valued split-radix FFT is presented, an algorithm that uses fewer operations than any otherreal-valued power-of-2-length FFT.
Journal ArticleDOI
Fourier Transform Study of NMR Spin-Lattice Relaxation by "Progressive Saturation"
Ray Freeman,Howard D. W. Hill +1 more
TL;DR: In this paper, a steady state is established where there is a dynamic balance between the effect of the pulses and spin relaxation, and the deviation of the intensity of the free induction signal from its thermal equilibrium value is an exponential function of the pulse interval with time constant equal to the spin-lattice relaxation time.
References
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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.
Proceedings ArticleDOI
Fast Fourier Transforms: for fun and profit
W. M. Gentleman,G. Sande +1 more
TL;DR: The "Fast Fourier Transform" has had a major effect on several areas of computing, the most striking example being techniques of numerical convolution, which have been completely revolutionized.
Journal ArticleDOI
Modern techniques of power spectrum estimation
TL;DR: In this paper, it is shown that the computationally fastest way to calculate mean lagged products is to begin by calculating all Fourier coefficients with a fast Fourier transform and then to fast-Fourier-retransform a sequence made up of a{k}^{2}+b_{k}−2} (where a_{k+ib_{k}) is the complex Fourier coefficient.
Journal ArticleDOI
On computing the fast Fourier transform
TL;DR: The fast Fourier transform algorithm is briefly reviewed and fast difference equation methods for accurately computing the needed trigonometric function values are given and the problem of computing a large Fouriertransform on a system with virtual memory is considered, and a solution is proposed.