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 implementation loss of a fast Fourier transform algorithm according to a bit truncation process is analyzed; the measured results show a better performance of truncation after FFT output.
Abstract: In this paper, we analyze an implementation loss of a fast Fourier transform algorithm according to a bit truncation process. A 4K-point FFT algorithm is proposed and implemented in field programmable gate arrays. Because bit cannot be extended indefinitely, the truncation is required and performance varies depending on the truncation method in the implementation of the FFT algorithm. We measure the implementation loss according to a bit truncation process; the measured results show a better performance of truncation after FFT output.
25 Jul 2004
TL;DR: A modified version of the very efficient sampling algorithm for finding a B-term Fourier representation of given 1D discrete signal, which can be applied to 2D signals is presented.
Abstract: Recently, a very efficient sampling algorithm for finding a B-term Fourier representation of given 1D discrete signal is presented (Gilbert et al., 2002). In this paper, we present a modified version of the algorithm, which can be applied to 2D signals. As in the original algorithm, dependence of the running time on the signal length is polylogarithmic.
TL;DR: This paper shows how a combination of the techniques of “redundancies” and “Kronecker decompositions” may be used with a specification for the data collection to produce a fast, accurate algorithm which solves the linear system.
Abstract: In a recently developed approach to the optical inverse scattering problem, the need arose to solve very large systems of linear equations with a nonsparse matrix. The entries in the matrix are determined by the specifications for the data collection pattern. The matrix is not a Discrete Fourier Transform matrix, and it not anenable to FFT methods. In this paper we show how a combination of the techniques of “redundancies” and “Kronecker decompositions” may be used with a specification for the data collection to produce a fast, accurate algorithm which solves the linear system. This algorithm has been implemented on a sequential computer, but parallel computation is clearly feasible.
31 May 1998
TL;DR: In this paper, an efficient prime factor algorithm for the discrete cosine transform (DFT) is introduced, where the decomposition is formulated directly, by using the proposed input and output mapping, and derive a novel in-place address generation scheme.
Abstract: An efficient prime factor algorithm for the discrete cosine transform is introduced. In this approach, we formulate the decomposition directly, by using the proposed input and output mapping, and derive a novel in-place address generation scheme, whilst the formulations in the literature require multiple stages or have to be done via the DFT. This approach requires one output index mapping only while the conventional algorithms require two mappings. Hence, by using the proposed mappings and address generation techniques, less temporary storage is required during the computation. A comparison of the address generation time between our approach and the conventional non-in-place approach is also shown.