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Prime-factor FFT algorithm
About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.
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TL;DR: In this paper, a new perspective for the IEEE standard 1459-2000 definitions is introduced using the stationary wavelet transform (SWT), which can provide variable frequency resolution while preserving time information without spectral leakage as the FFT.
Abstract: Power components, power factors, and pollution factor are defined according to the IEEE standard 1459-2000 based on the fast Fourier transform (FFT). However, the FFT in the presence of nonstationary power quality (PQ) disturbances results in inaccurate values due to its sensitivity to the spectral leakage problem. In this paper, a new perspective for the IEEE standard 1459-2000 definitions is introduced using the stationary wavelet transform (SWT). As a time-frequency transform, the SWT can provide variable frequency resolution while preserving time information without spectral leakage as the FFT. Moreover, unlike other time-frequency transforms, such as discrete wavelet transform (DWT), SWT possesses the time-invariance property that keeps the time and frequency characteristics throughout all of the decomposition levels. Results of different case studies including stationary, nonstationary of synthetic, and real PQ disturbances proves the effectiveness of applying the SWT over FFT or DWT.
95 citations
TL;DR: This paper deals with two's complement arithmetic with either rounding or chopping with eitherRoundoff errors for radix-2 FFT's and mixed-radix FFTs.
Abstract: A statistical model for roundoff errors is used to predict the output noise of the two common forms of the fast Fourier transform (FFT) algorithm, the decimations in-time and in-frequency. This paper deals with two's complement arithmetic with either rounding or chopping. The total mean-square errors and the mean-square errors for the individual points are derived for radix-2 FFT's. Results for mixed-radix FFT are also given.
93 citations
TL;DR: An extended split-radix fast Fourier transform (FFT) algorithm is proposed that has the same asymptotic arithmetic complexity as the conventional split- Radix FFT algorithm but has the advantage of fewer loads and stores.
Abstract: An extended split-radix fast Fourier transform (FFT) algorithm is proposed. The extended split-radix FFT algorithm has the same asymptotic arithmetic complexity as the conventional split-radix FFT algorithm. Moreover, this algorithm has the advantage of fewer loads and stores than either the conventional split-radix FFT algorithm or the radix-4 FFT algorithm.
90 citations
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.
Abstract: The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients. This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used. Upper and lower bounds for the total relative mean square error are given. The theoretical results are in good agreement with the actual error observed by taking the FFT of data sequences.
89 citations
TL;DR: The base 8 algorithms described in this paper allow one to perform as many base 8 iterations as possible and then finish the computation by performing a base 4 or a base 2 iteration if one is required, which preserves the versatility of the base 2 algorithm while attaining the computational advantage of thebase 8 algorithm.
Abstract: 1. Introduction. Cooley and Tukey stated in their original paper [1] that the Fast Fourier Transform algorithm is formally most efficient when the number of samples in a record can be expressed as a power of 3 (i.e., N = 3m), and further that there is little efficiency lost by using N = 2m or N = 4™. Later, however, it was recognized that the symmetries of the sine and cosine weighting functions made the base 4 algorithms more efficient than either the base 2 or the base 3 algorithms [2], [3]. Making use of this observation, Gentleman and Sande have constructed an algorithm which performs as many iterations of the transform as possible in a base 4 mode, and then, if required, performs the last iteration in a base 2 mode. Although this "4 + 2" algorithm is more efficient than base 2 algorithms, it is now apparent that the techniques used by Gentleman and Sande can be profitably carried one step further to an even more efficient, base 8 algorithm. The base 8 algorithms described in this paper allow one to perform as many base 8 iterations as possible and then finish the computation by performing a base 4 or a base 2 iteration if one is required. This combination preserves the versatility of the base 2 algorithm while attaining the computational advantage of the base 8 algorithm.
88 citations