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Article title TRUNCATION ERRORS OF THE RESULTS OF FIXED-POINT ARITHMETIC OPERATIONS IN THE FFT ALGORITHMS
Authors O.V. Yershova, A.V. Chkan, E.V. Kirichenko, E.A. Semernikov
Section SECTION II. MATHEMATICAL AND SOFTWARE OF SUPERCOMPUTERS
Month, Year 12, 2014 @en
Index UDC 004.382.2
DOI
Abstract The errors of decimation-in-frequency fast Fourier transform (DIF FFT) calculation (without scaling) caused by limitations of the length fixed-point results of arithmetic operations depending on the FFT size, the number of the spectrum component and the method of brining the result to the system word length (truncation or rounding) are considered. Analytic expressions of root-mean-square (RMS) errors of spectrum calculation both for truncation and rounding of the results of multiplication in the DIF FFT algorithm (without scaling) depending on the FFT size and the number of the spectrum component were obtained. It is shown that in the range of low frequency it is possible to use the dependence of the module of mathematical expectation of truncation errors from the number of a spectral sample for approximate estimation of the noise level caused by truncation of the results of arithmetic operations for the DIF FFT. The mathematical experiment was performed to calculate errors of arithmetic operations of FFT for a white Gaussian noise as the input process. The graphics of RMS value of truncation and rounding errors depending on the number of spectral component are presented. It is shown that the dependence of RMS value of truncation errors of arithmetic operations on the number of spectral component has asymmetrical behavior and lead to the significant spectrum distortions in the range of low frequency. The computational modeling has proved the matching of experimental and theoretical noise levels.

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Keywords The effect of the accumulation of errors; the fast fourier transform; error analysis; numerical modeling; digital signal processing.
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