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.

Computing the Fourier transform of real data on a hypercube

Abstract: There are two ways, other than the standard fast Fourier transform (FFT) algorithm, of computing Fourier transforms of real data, namely, (1)the real fast Fourier transform (RFFT) algorithm, and (2) the fast Hartley transform (FHT) algorithm. On a sequential computer, it has been shown that both the RFFT and the FHT algorithms are faster than the FFT algorithm. However, it is not obvious that the same is true on a parallel machine. The communication requirements of the RFFT and the FHT algorithms, which are critical to the cost of any parallel implementation, are different from those of the FFT algorithm. In this paper we present efficient implementations of the RFFT and the FHT algorithms on a hypercube machine. Experimental results are given for the implementation of the RFFT and the FHT algorithms on the NCUBE machine.

Generating and Searching Families of FFT Algorithms

Abstract: A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log n - 6n + 8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Recent work by Van Buskirk et al. demonstrated improvements to the split-radix operation count by using multiplier coefficients or "twiddle factors" that are not n-th roots of unity for a size-n DFT. This paper presents a Boolean Satisfiability-based proof of the lowest operation count for certain classes of DFT algorithms. First, we present a novel way to choose new yet valid twiddle factors for the nodes in flowgraphs generated by common power-of-two fast Fourier transform algorithms, FFTs. With this new technique, we can generate a large family of FFTs realizable by a fixed flowgraph. This solution space of FFTs is cast as a Boolean Satisfiability problem, and a modern Satisfiability Modulo Theory solver is applied to search for FFTs requiring the fewest arithmetic operations. Surprisingly, we find that there are FFTs requiring fewer operations than the split-radix even when all twiddle factors are n-th roots of unity.

A fast Fourier transform algorithm using Hadamard transform

Abstract: A fast Fourier transform (FT) algorithm using Hadamard transform (HT) is introduced, which is called HFT (Hadamard Fourier Transform). In the algorithm proposed here, a HT is used as mid-transform and the redundant calculation in the original fast FT algorithm is reduced by double transformation. The results of theoretical analysis show that the number of multiplications and additions of HFT are both decreased by 60% compared with that of traditional FFT and the executed result shows the computing speed of HFT is 1.6 to 1.7 times faster than FFT. Comparing with the similar algorithms such as WFT-II1, RFT2, it has a market improvement in computing speed and eliminates the limitatiom on the length of transform.

Method for improving computation precision in fast Fourier transform

Abstract: A method for improving precision in FFT calculations. For each iteration in an FFT implementation, a constant normalization multiplier is inserted such that the dynamic ranges of the input and output are the same. The final FFT output is multiplied by a constant normalization factor given by the number of iterations and the constant normalization multiplier.