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Journal ArticleDOI

A note on "An accurate error analysis model for fast Fourier transform"

01 Jun 1999-IEEE Transactions on Signal Processing (IEEE)-Vol. 47, Iss: 6, pp 1743-1744
TL;DR: Closed-form expressions for the correlation between errors of different stages have been derived and verified by comparing the predicted values using these expressions with the simulation values given by Ma.
Abstract: The expressions derived by Ma (see ibid., vol.45, p.1641, 1997) for error variance and average power expectation using the model that has been proposed are not accurate. In this paper, all the possible correlations have not been considered. The expressions have been modified to make them exact. Closed-form expressions for the correlation between errors of different stages have been derived. The expressions have been verified by comparing the predicted values using these expressions with the simulation values given by Ma.
Citations
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Journal ArticleDOI
TL;DR: From the simulation results, the radix-2 DIT FFT algorithm has better accuracy in term of signal-to-quantization-noise ratio (SQNR) and a simple criterion of wordlength optimization is proposed to yield comparable accuracy with fewer bit budget.
Abstract: In this paper, we investigate the effect of fixed-point arithmetics with limited precision for different fast Fourier transform (FFT) algorithms. A matrix representation of error propagation model is proposed to analyze the rounding effect. An analytic expression of overall quantization loss due to the arithmetic quantization errors is derived to compare the performance with decimation-in-time (DIT) and decimation-in-frequency (DIF) configurations. From the simulation results, the radix-2 DIT FFT algorithm has better accuracy in term of signal-to-quantization-noise ratio (SQNR). Based on the results, a simple criterion of wordlength optimization is proposed to yield comparable accuracy with fewer bit budget.

81 citations

Journal ArticleDOI
TL;DR: Deterministic models are used to determine the effect of quantization errors in radix-2 DIT-F HT and DIF-FHT algorithms and the problem of twiddle factor quantization is also considered independently in both DIT and Dif-Fht algorithms.

1 citations

References
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Journal ArticleDOI
TL;DR: An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm and an accurate error expression and error variance for the computation of FFT are derived.
Abstract: An error propagation model is proposed for the in-place decimation-in-time version of the radix-2 FFT algorithm. With the model, an accurate error expression and error variance for the computation of FFT are derived. This correspondence deals with fixed-point and block floating-point arithmetic. Simulation results agree closely with the theoretical predicted ones. We find that some roundoff errors at different stages correlate with each other. The density of correlations is closely associated with the round-off approach used in butterfly calculations.

28 citations