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 theorem combines the general conditions for the existence of number theoretic transforms in the rings of integers modulo m with two conditions for high computational efficiency.
Abstract: A new theorem that gives necessary and sufficient conditions for the existence of computationally fast number theoretic transforms is presented. The theorem combines the general conditions for the existence of number theoretic transforms in the rings of integers modulo m with two conditions for high computational efficiency.
3 citations
01 Sep 2004
TL;DR: The Fast Linear Canonical Transform (FLCT) is derived, a fast algorithm for its implementation using a similar approach as was done with the derivation of the Fast Fourier Transform (FFT) for implementation of the Discrete Fourier transform (DFT).
Abstract: The fractional Fourier transform (FRT) is a recently developed tool for linear space-frequency (or time-frequency) signal processing It is a generalisation of the Fourier transform, FT, has a simple optical implementation and can potentially find use wherever the FT is used We discuss and compare the most popular fast algorithms currently being used (in the area of optical signal processing, OSP) to calculate the digital FRT We develop theory for the discrete Linear Canonical Transform (LCT) of which the FRT is a special case We then derive the Fast Linear Canonical Transform (FLCT), a fast algorithm for its implementation using a similar approach as was done with the derivation of the Fast Fourier Transform (FFT) for implementation of the Discrete Fourier Transform (DFT) The new algorithm is entirely independent of the FFT and is based purely on the properties of the LCT and FRT
3 citations
01 May 1982
TL;DR: A new two dimensional DFT algorithm is given, the Mixed Simultaneous Decimation FFT algorithm, which can be used to perform decimation-in-time orDecimation-infrequency in both dimensions simultaneously.
Abstract: The well-known decimation-in-time and decimation-infrequency FFT algorithms have recently been combined into a single and more efficient one, the Mixed Decimation FFT algorithm. On the other hand, an efficient way to perform a two dimensional DFT computation is to use decimation-in-time or decimation-infrequency in both dimensions simultaneously. In this paper the above two ideas are combined to give a new two dimensional DFT algorithm, the Mixed Simultaneous Decimation FFT algorithm.
3 citations
TL;DR: The fast-Fourier transform (FFT) which processes a large amount of data, such as image, is considered, as a structure for the one-dimensional FFT processor, the constant-geometry type FFT algorithm and the bit-serial pipeline floating-point arithmetic are discussed.
Abstract: This paper considers the fast-Fourier transform (FFT) which processes a large amount of data, such as image. As a structure for the one-dimensional FFT processor, aiming at eliminating some restrictions in VLSI design, the constant-geometry type FFT algorithm and the bit-serial pipeline floating-point arithmetic are discussed. The major results are as follows. (1) Using the constant-geometry algorithm, the memory elements to perform the rearrangement characteristic to FFT can be realized by a uniform structure and uniform control scheme throughout the stages. The memory element for N-point FFT can be constructed as a simple and regular structure using 2 of N/2-stage shift-registers. (2) The multiplication cell with code extender, the serial structure of normalization circuit and the shifter, and the parallel operation covering a longer length than the input word length are employed. By those schemes, the pipeline operation of floatingpoint arithmetic is realized without a guard bit. By this scheme, the restriction in VLSI using the butterfly elements can be reduced drastically. (3) As an additional effect of the regular structure of the memory element, the automatic defecttolerant operation is made possible, using the effective k-out-of-n redundant structure and the self-testing. By this scheme, the restriction for the VLSI chip-area can be reduced when the number of sampling points is increased. (4) The one-dimensional FFT processor can be realized as a modular structure, which is a cascade connection of two kinds of VLSI, i. e., butterfly element and the memory elements.
3 citations
06 Apr 2014
TL;DR: The accuracy of the proposed choice is numerically assessed for an electromagnetic application consisting of the implementation of the aggregation and disaggregation steps in the fast calculation of the scattered field by the Fast Multipole Method.
Abstract: We discuss how the parameters of 1D Type 3 Non-Uniform Fast Fourier Transform (NUFFT) algorithms based on the Gaussian gridding can be chosen to achieve a prescribed accuracy. Type 3 NUFFT algorithms are of interest in many areas of applied electromagnetics, as for example fast antenna analysis and synthesis and fast calculation of the scattered fields. The approach is related to the one dimensional case and follows the work in A. Dutt and V. Rokhlin, SIAM J. Sci. Comp. 14 (1993). The accuracy of the proposed choice is numerically assessed for an electromagnetic application consisting of the implementation of the aggregation and disaggregation steps in the fast calculation of the scattered field by the Fast Multipole Method.
3 citations