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Split-radix FFT algorithm
About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.
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17 Oct 2011
TL;DR: Results show that multigrid-based methods begin to outperform FFT-based ones for N∼103 and the constant in front of their asymptotic complexity estimate is larger and their accuracy-efficiency tradeoffs are different.
Abstract: The effectiveness of multigrid and fast Fourier transform (FFT) based methods are investigated for accelerating the solution of volume integral equations encountered in bioelectromagnetics (BIOEM) analysis. The typical BIOEM simulation is in the mixed-frequency regime of analysis because the field variations in the simulation domain are dictated by a combination of the free space wavelength, geometrical features, and the wavelengths/skin depths in tissues. In this case, multigrid-based methods (when appropriately truncated at high-frequency levels) can achieve O(N) complexity that is asymptotically superior to the O(NlogN) complexity of FFT-based ones. Nevertheless, the constant in front of their asymptotic complexity estimate is larger and their accuracy-efficiency tradeoffs are different. Numerical experiments are performed to compare these methods and the results show that multigrid-based methods begin to outperform FFT-based ones for N∼103.
16 citations
IBM1
TL;DR: In this article, a multi-dimensional discrete Fourier series method has been developed to calculate the coupling capacitances in VLSI circuits, which is related to the known electric potential distributions by Laplace equation.
Abstract: A multi-dimensional discrete Fourier series method has been developed to calculate the coupling capacitances in VLSI circuits. In the present method a scalar potential Φ( r ) is generated, in discrete Fourier series form, which is related to the known electric potential distributions by Laplace equation. By using the multiple radix Fast Fourier Transform (FFT) algorithm to reduce the CPU time, the electric field strength can be obtained from the gradient of the scalar potential. The calculated 2-D and 3-D results generally compare well with the conventional approach results. A program has been developed and numerical results are discussed.
16 citations
Patent•
27 Aug 1996
TL;DR: In this paper, the smallest possible circuit size is provided for FFT computing units, FFT computation devices, and pulse counters that can achieve computational precision using the smallest available circuit size.
Abstract: To provide FFT computing units, FFT computation devices, and pulse counters that can achieve computational precision using the smallest possible circuit size. FFT computing unit 602 comprises a data shift circuit for standardizing FFT computation target data to a specified bit width, adders/subtracters, multipliers, and data converters for standardizing the bit width to a certain bit width by truncating part of the output data of each computing unit, etc. FFT computation device comprises FFT computing unit 602, sensor 620, amplification circuit 621, gain control circuit 623, AD converter 622, first RAM 625 for sequentially storing the A/D conversion data, second RAM 626 for storing the FFT computation target data and the data being computed, coefficient ROM 101, and level determination circuit 624; and the level determination circuit determines the size of the data being transferred when the data is being transferred from RAM 1 to RAM 2, and the result is used for the data shift adjustment and gain control during FFT computation.
15 citations
03 May 1982
TL;DR: A highly effective dynamic programming algorithm is presented as a solution to the problem of finding an algorithm from this class which is optimal with respect to the specific add, multiply, and data transfer characteristics of a partlcular implementation.
Abstract: A broad class of efficient, discrete Fourier transform algorithms is developed by partitioning short DFT algorithms into factors. The factored short DFT's are combined into longer DFT's using a prime factor algorithm (PFA). By exploiting a property which allows some of the factors to commute, a large set of possible DFT algorithms is generated which contains both the prime factor algorithm and the Winograd Fourier Transform Algorithm (WFTA) as special cases. The problem of finding an algorithm from this class which is optimal with respect to the specific add, multiply, and data transfer characteristics of a partlcular implementation is posed, and a highly effective dynamic programming algorithm is presented as a solution.
15 citations
TL;DR: The algorithms developed in this paper update the DFT to reflect the modified window contents, using less computation than directly evaluating the modified transform via the FFT algorithm, which reduces the computational order by a factor of log 2 N for both the 1-D and 2-D cases.
15 citations