Journal ArticleDOI
Bounds on Error Due to Finite Arithmetic in FFT Computation
TLDR
It is shown that there are position-dependent bounds on the error amplitude in the Fourier co-efficients, which means that the error statistics are position dependent and the earlier results on finite arithmetic effects in FFT calculation are inaccurate to that extent.Abstract:
For the decimation-in-frequency FFT algorithm using fixed point arithmetic, it is shown that there are position-dependent bounds on the error amplitude in the Fourier co-efficients. This means that the error statistics are position dependent and the earlier results on finite arithmetic effects in FFT calculation are inaccurate to that extent. These results lead to worst-case deterministic design of FFT processor.read more
Citations
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Incertitudes de calcul dans un processeur de Fourier rapide modélisation et expérience Error analysis of a floating block FFT processor : model and experiment
TL;DR: Par iteration sur l'ensemble des etapes, cette analyse mene a l'estimation de l'energie des trois contributions d'erreur erreurs d'entree, arithmetique and de coefficients qui sont comparees a l'sexperience.
References
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Journal ArticleDOI
Effects of finite register length in digital filtering and the fast Fourier transform
Alan V. Oppenheim,C. Weinstein +1 more
TL;DR: The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff, to illustrate techniques of working with particular models.
Journal ArticleDOI
Accumulation of Round-Off Error in Fast Fourier Transforms
Toyohisa Kaneko,Bede Liu +1 more
TL;DR: This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used, and upper and lower bounds for the total relative meansquare error are given.
Journal ArticleDOI
Roundoff error analysis of the fast Fourier transform
TL;DR: In this paper, an analysis of roundoff errors occurring in the floating-point computation of the fast Fourier transform is presented, and upper bounds for the ratios of the root-mean-square (RMS) and maximum roundoff error in the output data to the RMS value of the input data for both single and multidimensional transformations are derived.