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: An improved algorithm is presented in which by use of polynomial curve fitting method the processing of the peripheral frequency band of the spectral is carried out at the both sides of the zero setting area of the original threshold value method, so the algorithm can adapt the DSI in a wider frequency band.
Abstract: The suppression of discrete spectral interference (DSI) is always an important topic in on-line partial discharge monitoring and for this purpose many digital signal processing methods are put forward. Based on the research of the threshold value method of frequency domain in fast Fourier transform, an improved algorithm is presented in which by use of polynomial curve fitting method the processing of the peripheral frequency band of the spectral is carried out at the both sides of the zero setting area of the original threshold value method, so the algorithm can adapt the DSI in a wider frequency band. The results from simulation and measured data indicate that using this algorithm a better interference suppression can be obtained.
4 citations
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TL;DR: It is shown that CORDIC can be efficiently used in twiddle factor calculation of the Radix-4 FFT algorithm and can be widely used in large size of FFT like OFDM Modem.
Abstract: In this paper, an efficient butterfly structure for 8K/2K-Point Radix-4 FFT algorithm using CORDIC(coordinate rotation digital computer) is proposed. It is shown that CORDIC can be efficiently used in twiddle factor calculation of the Radix-4 FFT algorithm. The Verilog-HDL coding results for the proposed CORDIC butterfly structure show 36.9% cell area reduction comparison with those of the conventional multiplier butterfly structure. Furthermore, the 8K/2K-point Radix-4 pipeline structure using the proposed butterfly and delay commutators is compared with other conventional structures. Implementation coding results show 11.6% cell area reduction. Due to its efficient processing scheme, the proposed FFT structure can be widely used in large size of FFT like OFDM Modem.
4 citations
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01 Jan 2005
TL;DR: The principal topics of this thesis are generalizations and applications of the NFFT and a new robust local scattered data approximation method that generalizes an approach of van den Boomgard and van de Weijer to scattered data.
Abstract: The direct computation of the discrete Fourier transform at arbitrary nodes requires O(NM) arithmetical operations, too much for practical purposes. For equally spaced nodes the computation can be done by the well known fast Fourier transform (FFT) in only O(N log N) arithmetical operations. Recently, the fast Fourier transform for nonequispaced nodes (NFFT) was developed for the fast approximative computation of the above sums in only O(N log N + M log 1/e), where e denotes the required accuracy. The principal topics of this thesis are generalizations and applications of the NFFT. This includes the following subjects: - Algorithms for the fast approximative computation of the discrete cosine and sine transform at nonequispaced nodes are developed by applying fast trigonometric transforms instead of FFTs. - An algorithm for the fast Fourier transform on hyperbolic cross points with nonequispaced spatial nodes in 2 and 3 dimensions based on the NFFT and an appropriate partitioning of the hyperbolic cross is proposed. - A unified linear algebraic approach to recent methods for the fast computation of matrix-vector-products with special dense matrices, namely the fast multipole method, fast mosaic-skeleton approximation and H-matrix arithmetic, is given. Moreover, the NFFT-based summation algorithm by Potts and Steidl is further developed and simplified by using algebraic polynomials instead of trigonometric polynomials and the error estimates are improved. - A new algorithm for the characterization of engineering surface topographies with line singularities is proposed. It is based on hard thresholding complex ridgelet coefficients combined with total variation minimization. The discrete ridgelet transform is designed by first using a discrete Radon transform based on the NFFT and then applying a dual-tree complex wavelet transform. - A new robust local scattered data approximation method is introduced. It is an advancement of the moving least squares approximation (MLS) and generalizes an approach of van den Boomgard and van de Weijer to scattered data. In particular, the new method is space and data adaptive.
4 citations
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24 May 1993
TL;DR: The relationship among four different versions of the DFT and their inherent properties are explored and the new real-multiplier FFT-j algorithms are proposed for all four version of the N=2/sup m/ DFT.
Abstract: In this paper four different versions of the DFT (DFT-j,j=I,II,III,IV) are first introduced, Then, the relationship among four different versions of the DFT and their inherent properties are explored. The new real-multiplier FFT-j algorithms are proposed for all four versions of the N=2/sup m/ DFT. The algorithm formulae are derived, represented by Kronecker product and direct sum. Finally, the signal flowgraph for the length-2/sup 3/ FFT-j is given to illustrate the proposed algorithms. The computational complexity is analysed and a comparison is made with other existing real-multiplier FFT algorithms. The proposed algorithms require the minimum number of arithmetic operations and use real multipliers and allow in-place computation. Besides, the proposed algorithms have very simple and regular structure. They have been implemented by software and have been finding practical applications. >
4 citations
01 Jan 2015
TL;DR: A comparison of area and minimum time delay are drawn between the proposed design of 32 point FFT by using Mixed-Radix algorithm with Radix-2 algorithm to implement Mixed Radix 32-point F FT by using hardware language (VHDL).
Abstract: This paper focus on the development of the fast Fourier transform (FFT), based on Decimation-In-Time (DIT) domain by using Mixed-Radix algorithm (Radix-4 and Radix-8).Fast Fourier transforms, popularly known as FFTs, have become an integral part of any type of digital communication system and a wide variety of approaches have been tried in order to optimize the algorithm for a variety of parameters such as area, time delay, power and speed. In this paper a comparison of area and minimum time delay are drawn between the proposed design of 32 point FFT by using Mixed-Radix algorithmwithRadix-2 algorithm. Here our goal is to implement Mixed Radix 32-point FFT by using hardware language (VHDL). Simulation and synthesis of design is done using Xilinx ISE 14.7. The result shows significant reduction in terms of area complexity and minimum time delay.
4 citations