Journal ArticleDOI
Accumulation of roundoff errors in floating point FFT
Tran Thong,Bede Liu +1 more
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TLDR
A statistical model for roundoff error is used to predict the output noise to signal ratio of the two common FFT algorithms, the decimation in time and the decimating in frequency algorithms.Abstract:
A statistical model for roundoff error is used to predict the output noise to signal ratio of the two common FFT algorithms, the decimation in time and the decimation in frequency algorithms. A unified approach is used to obtain the error in both algorithms. Results for radix 2 and for arbitrary radix are presented. Multidimensional FFT is also discussed.read more
Citations
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Journal ArticleDOI
Floating point error analysis of two-dimensional, fast Fourier transform algorithms
TL;DR: In this article, the authors conducted a comparison of three algorithms commonly used for the calculation of two-dimensional fast Fourier transforms (FFTs), namely, the conventional row-column FFT, the vector-radix FFT and the polynomial-transform FFT.
Journal ArticleDOI
Real-time generation of atmospheric turbulence phase screen with non-uniform fast Fourier transform
TL;DR: In this paper, a non-uniform fast Fourier transform technique is proposed to accelerate phase screen generation speed, which is able to generate huge atmospheric turbulence phase screens with high fidelity and an acceptable time-cost enabling practical adaptive optics simulations of forthcoming Extremely Large Telescopes.
Journal ArticleDOI
Results of a deterministic analysis of FFT coefficient errors
TL;DR: In this article, a deterministic approach towards the analysis of coefficient errors in DFT and FFT was proposed, and detailed results were presented in a compact "necessary wordlength for prescribed criteria and output accuracy" form.
Journal ArticleDOI
A software for evaluating local accuracy in the fourier transform
P. Bois,Jean Vignes +1 more
TL;DR: A software based on the Perturbation Method for estimating the local accuracy in the Fast Fourier Transform, both in the case of exact data and experimental data, is proposed.
Book ChapterDOI
Fast Fourier Transforms
TL;DR: The chapter presents a comparison of number of arithmetic operations required to compute various FFT algorithms and presents a simple, easy to visualize graphical techniques i to specify digital word lengths in a typical spectral analysis system.
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.
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.
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
What is the fast Fourier transform
W.T. Cochran,J.W. Cooley,D.L. Favin,H. Helms,R. A. Kaenel,W.W. Lang,G. Maling,D.E. Nelson,C. Rader,Peter D. Welch +9 more
TL;DR: The discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method for computing this transform is derived, and some of the computational aspects of the method are presented.
Book
Floating Point Computation
TL;DR: Write a function in a programming language of your choice that takes a (32-bit IEEE format) float and returns a float with the property that: given zero, infinity or a positive normalised floating-point number then its result is the smallest normalised Floating Point Number greater than its argument.