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: For certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably by performing the cyclic convolution with the Mersenne prime number-theoretic transform developed originally by Rader.
Abstract: In this paper for certain long transform lengths, Winograd's algorithm for computing the discrete Fourier transform (DFT) is extended considerably. This is accomplisbed by performing the cyclic convolution, required by Winograd's method, with the Mersenne prime number-theoretic transform developed originally by Rader. This new algorithm requires fewer multiplications than either the standard fast Fourier transform (FFT) or Winograd's more conventional algorithm. However, more additions are required.
10 citations
TL;DR: The focus is on studying the analog of the Cooley-Tukey algorithm because the number of operations applied to calculate the n-dimensional FFT is considerably less than in the conventional algorithm.
Abstract: The one-dimensional fast Fourier transform (FFT) is the most popular tool for calculating the multidimensional Fourier transform. As a rule, to estimate the n-dimensional FFT, a standard method of combining one-dimensional FFTs, the so-called "by rows and columns" algorithm, is used in the literature. For fast calculations, different researchers try to use parallel calculation tools, the most successful of which are searches for the algorithms related to the computing device architecture: cluster, video card, GPU, etc. [1, 2]. The possibility of paralleling another algorithm for FFT calculation, which is an n-dimensional analog of the Cooley-Tukey algorithm [3, 4], is studied in this paper. The focus is on studying the analog of the Cooley-Tukey algorithm because the number of operations applied to calculate the n-dimensional FFT is considerably less than in the conventional algorithm nN n log2 N of addition operations and 1/2N n + 1log2 N of multiplication operations of addition operations and $$\frac{{2^n - 1}} {{2^n }}N^n \log _2 N$$ of multiplication operations against: N n + 1log2 N of addition operations and 1/2N n + 1log2 N of in combining one-dimensional FFTs.
10 citations
TL;DR: The present method can be implemented in the microprocessor and VLSI environment using a commercial FFT chip and yields energy preserving and shift invariant decimated analytic wavelet coefficients, which are free of aliasing effects.
Abstract: This letter introduces an analytic wavelet transform based on linear phase quadrature mirror filters (QMFs). The computation of the analytic signal and the reconstruction of the signal is carried by the fast Fourier transform (FFT)-based algorithm. The transform yields energy preserving and shift invariant decimated analytic wavelet coefficients, which are free of aliasing effects. The present method can be implemented in the microprocessor and VLSI environment using a commercial FFT chip
10 citations
TL;DR: A generalization of the one-bin sliding parametric discrete Fourier transform is proposed, which significantly reduces the number of operations required for the algorithm to enter the sliding measurement mode.
Abstract: The basic methods of detecting individual tonal components and algorithms for their implementation are considered; their advantages and disadvantages are analyzed. A generalization of the one-bin sliding parametric discrete Fourier transform is proposed. The algorithm implementing this transformation significantly reduces the number of operations required for the algorithm to enter the sliding measurement mode.
10 citations
TL;DR: A RAG-n fast discrete Fourier transform will be shown to be of low latency and complexity and posses a VLSI attractive regular data flow when implemented with the Bluestein chirp-z algorithm.
Abstract: DFT and FFTs are important but resource intensive building blocks and have found many application in communication systems ranging from fast convolution to coding of OFDM signals. It has recently be shown that the n-Dimensional Reduced Adder Graph (RAG-n) technique is beneficially in many applications such as FIR or IIR filters, where multiplier can be grouped in multiplier blocks. This paper explores how the RAG-n technique can be applied to DFT algorithms. A RAG-n fast discrete Fourier transform will be shown to be of low latency and complexity and posses a VLSI attractive regular data flow when implemented with the Bluestein chirp-z algorithm. VHDL code synthesis results for Xilinx Virtex II FPGAs are provided and demonstrate the superior properties when compared with Xilinx FFT IP cores. Index Terms – Fast Fourier Transform, OFDM, FPGA, n-Dimensional Reduced Adder Graph
10 citations