Accumulation of Round-Off Error in Fast Fourier Transforms-Reference-Cited by-同舟云学术

Accumulation of Round-Off Error in Fast Fourier Transforms

Published:1970-10 Issue:4 Volume:17 Page:637-654
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Kaneko Toyohisa¹,Liu Bede²

Affiliation:

1. IBM, Thomas J. Watson Research Center, Yorktown Heights, New York and Princeton University, Department of Electrical Engineering, Princeton, New Jersey

2. Princeton University, Department of Electrical Engineering, Princeton, New Jersey

Abstract

The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients. This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used. Upper and lower bounds for the total relative mean square error are given. The theoretical results are in good agreement with the actual error observed by taking the FFT of data sequences.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/321607.321613

Reference15 articles.

1. Modern techniques of power spectrum estimation;BINGHAM C.;IEEE Trans. A U-15,1967

2. COCHRAN W.T. ETAL. WhatisthefastFouriertransform?Proc.IEEE55 10(Oct. 1967) 1644-1673. COCHRAN W.T. ETAL. WhatisthefastFouriertransform?Proc.IEEE55 10(Oct. 1967) 1644-1673.

3. An algorithm for the machine calculation of complex Fourier series;COOLEY J. W.;Math. Comput.,1965

4. Spectrum analysis in speech coding;FLANAOAN J.L;IEEE Trans. AU-15,1967

5. FORSYTHE G. AN D MOLER C.B. Computer Solution of Linear Algebraic Systems. Prentice-Hall Englewood Cliffs N. J. 1967. FORSYTHE G. AN D MOLER C.B. Computer Solution of Linear Algebraic Systems. Prentice-Hall Englewood Cliffs N. J. 1967.

Cited by 62 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A novel automatic segmentation method directly based on magnetic resonance imaging K-space data for auxiliary diagnosis of glioma;Quantitative Imaging in Medicine and Surgery;2024-02

2. Legendre Series Analysis and Computation via Composed Abel–Fourier Transform;Symmetry;2023-06-19

3. ANALYSIS OF THE ERROR OF COMPUTATION FAST TRANSFORMS OF FOURIER CLASS BASED ON CYCLIC CONVOLUTIONS;Ukrainian Journal of Information Technology;2020

4. Correcting soft errors online in fast fourier transform;Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis;2017-11-12

5. Numerical approximation of oscillatory integrals of the linear ship wave theory;Applied Numerical Mathematics;2017-05