Journal ArticleDOI
Roundoff noise in floating point fast Fourier transform computation
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TLDR
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, 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.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}N where N is 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.read more
Citations
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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
Fault-tolerant FFT networks
J.-Y. Jou,Jacob A. Abraham +1 more
TL;DR: Two concurrent error detection (CED) schemes are proposed for N-point fast Fourier transform (FFT) networks that consists of log/sub 2/N stages with N/2 two-point butterfly modules for each stage to achieve both error detection and location.
Journal ArticleDOI
Effect of finite word length on the accuracy of digital filters--a review
TL;DR: The calculation of the statistical mean-squared error at the output of the filter is discussed in detail and some of the approaches used in investigating them are reviewed.
Journal ArticleDOI
Algorithm-based fault detection for signal processing applications
A.L.N. Reddy,Prithviraj Banerjee +1 more
TL;DR: A functional-level concurrent error-detection scheme is presented for such VLSI signal processing architectures as those proposed for the FFT and QR factorization, and it is shown that the error coverage is high with large word sizes.
Journal ArticleDOI
Algorithm-based fault tolerance on a hypercube multiprocessor
Prithviraj Banerjee,J.T. Rahmeh,Craig B. Stunkel,V.S.S. Nair,Kaushik Roy,V. Balasubramanian,Jacob A. Abraham +6 more
TL;DR: The authors propose the detection and location of faulty processors concurrently with the actual execution of parallel applications on the hypercube using a novel scheme of algorithm-based error detection, which allows the authors to isolate and replace faulty processors with spare processors.
References
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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.
Journal ArticleDOI
A fixed-point fast Fourier transform error analysis
TL;DR: In this article, an analysis of the fixed-point accuracy of the power of two, fast Fourier transform algorithm is presented, which leads to approximate upper and lower bounds on the root-mean-square error.
A Fixed-point Fast Fourier Transf orrn Error Analysis
TL;DR: In this article, an analysis of the fixed-point accuracy of the sequence power of two, fast Fourier transform algorithm is presented, which leads to approximate upper and lower bounds on the root-mean-square error.