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.
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TL;DR: The fast Fourier transform was investigated for potential use in a new application: the system identification problem in physiological transport models and was found to offer specific advantages when compared to another well-established transform technique, time segment transformation (TST).
8 citations
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29 Jun 2007
TL;DR: In this article, a general formulation and an associated design discipline for the two lattices are developed, which involves jointly determining element spacing, steering range and beam-layout geometry, grating-lobe behavior, and FFT factorability and therefore computational efficiency.
Abstract: : It is well known that when the identical elements of a planar receive array are laid out in horizontal rows and vertical columns, a fast Fourier transform or FFT can be used to efficiently realize simultaneous beams laid out in rows and columns in the direction cosines associated with the azimuth and elevation directions. Here a more general formulation and an associated design discipline is developed. Identical elements are laid out on an arbitrary planar lattice -- it could be square, rectangular, diamond, or triangular and might display tremendous symmetry or vary little -- and the beams in direction-cosine space are laid out on an arbitrary superlattice of the dual of the element-layout lattice. The generality of these two arbitrary lattice can yield significant cost reductions for large, many-beam arrays and arises from, first, formulating the desired beam outputs using a discrete Fourier transform or DFT generalized to use an integer-matrix size parameter, and second, efficiently realizing the required real-time computations with the generalized FFT based on a matrix factorization of that size parameter that is developed here. This generalized FFT includes as special cases the usual 1D and 2D FFTs in radix-2 and mixed-radix forms but offers many more possibilities as well. The approach cannot outperform but does match, when the matrix size parameter factors well, the N log N computational efficiency of the usual FFT. Examples illustrate a design discipline for the two lattices that involves jointly determining element spacing, steering range and beam-layout geometry, grating-lobe behavior, and FFT factorability and therefore computational efficiency.
8 citations
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TL;DR: An in-place version of the FFT is presented which takes a real sequence in natural order and produces the transform in scrambled order, which requires half of the operations and storage of the complex algorithms.
Abstract: It has long been known that an in-place version of the Fast Fourier Transform (FFT) exists for real sequences of data. More recently, in-place FFTs have been devised for real sequences with even, odd, or quarter wave symmetries. All of these symmetric FFTs take the input sequence in scrambled (bit-reversed) order and produce the transform sequence in natural order. For many applications, this is the opposite of what is needed, i.e., one would like to provide the input sequence in natural order. In this paper, an in-place version of the FFT is presented which takes a real sequence in natural order and produces the transform in scrambled order. The algorithm requires half of the operations and storage of the complex algorithms. Analogous in-place algorithms are also given for naturally ordered even, odd, quarter wave even and quarter wave odd sequences.
8 citations
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01 Mar 2017TL;DR: This work extends a recent method for computing a periodized fast multipole method with an adaptive algorithm that reduces the required number of multipole-to-local and local- to-local translations by an order of magnitude, and results in an algorithm that is competitive with other nonuniform fast Fourier transforms.
Abstract: The nonuniform fast Fourier transform comprises a set of algorithms which approximately interpolate the usual discrete Fourier transform in the time and/or frequency domain. A nonuniform fast Fourier transform based on the fast multipole method was previously developed but passed over in favor of other approaches [1, 2]. This work extends a recent method for computing a periodized fast multipole method [3] with an adaptive algorithm that reduces the required number of multipole-to-local and local-to-local translations by an order of magnitude. This combination improves the speed and accuracy of the original algorithm, and results in an algorithm that is competitive with other nonuniform fast Fourier transforms. Numerical experiments are carried out comparing our implementation with others, demonstrating its viability.
8 citations
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TL;DR: In this paper, a formula for interpolation between output samples of a fast Fourier transform (FFT) is derived for obtaining greater frequency resolution when two coarse FFT outputs are available.
Abstract: A formula is derived for interpolation between output samples of a fast Fourier transform (FFT), i.e., in the frequency domain. Such a formula is useful for obtaining greater frequency resolution when two coarse FFT outputs are available. Consideration is also given to the effect of such interpolation on a weighted FFT.
8 citations