Topic
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.
Papers published on a yearly basis
Papers
More filters
12 Nov 2000
TL;DR: An algorithm for approximating the quantum Fourier transform over an arbitrary Z/sub p/ which requires only O(n log n) steps where n=log p to achieve an approximation to within an arbitrary inverse polynomial in n is given.
Abstract: We give an algorithm for approximating the quantum Fourier transform over an arbitrary Z/sub p/ which requires only O(n log n) steps where n=log p to achieve an approximation to within an arbitrary inverse polynomial in n. This improves the method of A.Y. Kitaev (1995) which requires time quadratic in n. This algorithm also leads to a general and efficient Fourier sampling technique which improves upon the quantum Fourier sampling lemma of L. Hales and S. Hallgren (1997). As an application of this technique, we give a quantum algorithm which finds the period of an arbitrary periodic function, i.e. a function which may be many-to-one within each period. We show that this algorithm is efficient (polylogarithmic in the period of the function) for a large class of periodic functions. Moreover, using standard quantum lower-bound techniques, we show that this characterization is right. That is, this is the maximal class of periodic functions with an efficient quantum period-finding algorithm.
162 citations
TL;DR: In this paper, an alternative form of the fast Fourier transform (FFT) is developed, which has the peculiarity that none of the multiplying constants required are complex-most are pure imaginary.
Abstract: An alternative form of the fast Fourier transform (FFT) is developed. The new algorithm has the peculiarity that none of the multiplying constants required are complex-most are pure imaginary. The advantages of the new form would, therefore, seem to be most pronounced in systems for which multiplication are most costly.
161 citations
TL;DR: In this article, a new algorithm to eliminate the error caused by this decaying component in the Fourier algorithm has been proposed, and three simplified methods are proposed to alleviate the computation burden.
Abstract: The impact of exponentially decaying direct component on the Fourier algorithm is theoretically investigated first in this paper. A new algorithm to eliminate the error caused by this decaying component in the Fourier algorithm has been proposed. Furthermore, three simplified methods are proposed to alleviate the computation burden. The performance of the Fourier algorithm improved with these methods along with the least error squares algorithm is evaluated using a simple network and a real power system modeled by EMTP. The evaluation results are presented and discussed.
156 citations
TL;DR: The sparse Fourier transform (SFT) addresses the big data setting by computing a compressed Fouriertransform using only a subset of the input data, in time smaller than the data set size.
Abstract: The discrete Fourier transform (DFT) is a fundamental component of numerous computational techniques in signal processing and scientific computing. The most popular means of computing the DFT is the fast Fourier transform (FFT). However, with the emergence of big data problems, in which the size of the processed data sets can easily exceed terabytes, the "fast" in FFT is often no longer fast enough. In addition, in many big data applications it is hard to acquire a sufficient amount of data to compute the desired Fourier transform in the first place. The sparse Fourier transform (SFT) addresses the big data setting by computing a compressed Fourier transform using only a subset of the input data, in time smaller than the data set size. The goal of this article is to survey these recent developments, explain the basic techniques with examples and applications in big data, demonstrate tradeoffs in empirical performance of the algorithms, and discuss the connection between the SFT and other techniques for massive data analysis such as streaming algorithms and compressive sensing.
154 citations
[...]
TL;DR: The Fast Fourier Transform (FFT) algorithm as discussed by the authors is the most well known vectorization algorithm for the discrete complex Fourier transform (DCFT). But it is not a generalization of the slow transform.
Abstract: Publisher Summary This chapter provides an overview on vectorizing the FFTs. The fast Fourier transform (FFT) is the most well known of all algorithms. It is superior to the slow transform and has applications in all areas of scientific computing. The term FFT was applied to a specific algorithm for the rapid computation of the discrete complex Fourier transform; however, it has become a generic term that is applied to any one of a large number of algorithms that compute the complex as well as other Fourier transforms. Many algorithms exist for a given Fourier transform, and when they are applied to a particular sequence, the result is the same. However, the algorithms differ in the ways that intermediate results are computed and stored. It is these important differences that provide the algorithms with unique properties that make one or the other more attractive for a particular application.
151 citations