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Roundoff noise in floating point fast Fourier transform computation

Content Provider	IEEE Xplore Digital Library
Author	Weinstein, C.
Copyright Year	1966
Abstract	A statistical model for roundoff errors is used to predict output noise-to-signal ratio when a fast Fourier transform is computed using floating point arithmetic. The result, derived for the case of white input signal, is that the ratio of mean-squared output noise to mean-squared output signal varies essentially as\nu = \log_{2}NwhereNis the number of points transformed. This predicted result is significantly lower than bounds previously derived on mean-squared output noise-to-signal ratio, which are proportional to ν². The predictions are verified experimentally, with excellent agreement. The model applies to rounded arithmetic, and it is found experimentally that if one truncates, rather than rounds, the results of floating point additions and multiplications, the output noise increases significantly (for a given ν). Also, for truncation, a greater than linear increase with ν of the output noise-to-signal ratio is observed; the empirical results seem to be proportional to ν², rather than to ν.
Starting Page	209
Ending Page	215
Page Count	7
File Size	702769
File Format	PDF
ISSN	00189278
Volume Number	17
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1969-09-01
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fast Fourier transforms Signal to noise ratio Discrete Fourier transforms Roundoff errors Floating-point arithmetic Predictive models Laboratories Upper bound Integrated circuit noise Digital filters
Content Type	Text
Resource Type	Article
Subject	Signal Processing Engineering Electrical and Electronic Engineering

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