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: This paper presents a fast Fourier transform (FFT) algorithm for computing length-q×2m DFTs, and the proposed algorithm achieves reduction of arithmetic complexity over the related algorithms.
Abstract: Discrete Fourier transform (DFT) is widely used in almost all fields of science and engineering. Fast Fourier transform (FFT) is an efficient tool for computing DFT. In this paper, we present a fast Fourier transform (FFT) algorithm for computing length- $q\times 2^{m}$ DFTs. The algorithm transforms all $q$ -points sub-DFTs into three parts. In the second part, the operations of subtransformation contain only multiplications by real constant factors. By transformation, length- $2^{m}$ -scaled DFTs (SDFT) are obtained. An extension of scaled radix-2/8 FFT (SR28FFT) is presented for computing these SDFTs, in which, the real constant factors of SDFTs are attached to the coefficients of sub-DFTs to simplify multiplication operations. The proposed algorithm achieves reduction of arithmetic complexity over the related algorithms. It can achieve a further reduction of arithmetic complexity for computing a length- $N=q\times 2^{m}$ IDFT by $2N-4m$ real multiplications. In addition, the proposed algorithm is applied to real-data FFT, and is extended to $6^{m}$ DFTs.
18 citations
05 Jul 2006
TL;DR: Experimental results have shown that the MFS features are suitable for Arabic character recognition and can be improved by using the "hole" feature of a character and use cleaning corrupted data.
Abstract: Arabic character recognition algorithm using Modified Fourier Spectrum (MFS) is presented. The MFS descriptors are estimated by applying the Fast Fourier Transform (FFT) to the Arabic character primary part contour. Ten descriptors are estimated from the Fourier spectrum of the character primary part contour by subtracting the imaginary part from the real part (and not from the amplitude of the Fourier spectrum as is usually the case). These descriptors are then used in the training and testing of Arabic characters. The computation of the MFS descriptors requires less computation time than the computation of the Fourier descriptors. Experimental results have shown that the MFS features are suitable for Arabic character recognition. Average recognition rate of 95.9% was achieved for the model classes. The analysis of the errors indicates that this recognition rate can be improved by using the "hole" feature of a character and use cleaning corrupted data.
17 citations
01 Dec 1999
TL;DR: This paper presents an efficient implementation of the pipeline FFT processor based on the radix-4 decimation-in-time algorithm with the use of digit-serial arithmetic units that can not only achieve nearly 100% hardware utilization, but also require much less memory compared with the previous digit- serial FFT processors.
Abstract: This paper presents an efficient implementation of the pipeline FFT processor based on the radix-4 decimation-in-time algorithm with the use of digit-serial arithmetic units. By splitting the sequential input sample into parallel digit-serial data streams, the proposed architecture can not only achieve nearly 100% hardware utilization, but also require much less memory compared with the previous digit-serial FFT processors. Furthermore, in FFT processors, several modules of ROM are required for the storage of twiddle factors. By exploiting the redundancy of the factors, the overall ROM size can be effectively reduced by a factor of 2.
17 citations
TL;DR: In this article, the authors conducted a comparison of three algorithms commonly used for the calculation of two-dimensional fast Fourier transforms (FFTs), namely, the conventional row-column FFT, the vector-radix FFT and the polynomial-transform FFT.
Abstract: Floating-point error is conducted for three algorithms commonly used for the calculation of two-dimensional fast Fourier transforms (FFTs), namely, the conventional row-column FFT, the vector-radix FFT, and the polynomial-transform FFT The respective errors are determined both analytically and on the basis of computer simulation Comparison shows that the vector-radix FFT and the polynomial-transform FFT, even though computationally more efficient than the row-column FFT, show approximately the same (and sometimes reduced) susceptibility to errors in floating-point arithmetic >
17 citations
01 Jan 2013
TL;DR: In this paper, the authors investigated discrete Fourier transform (DFT) and Fast Fourier Transform (FFT) algorithms to compute signal amplitude spectrum and power spectrum, and used the window function to reduce spectral leakage.
Abstract: This chapter investigates discrete Fourier transform (DFT) and fast Fourier transform (FFT) and their properties; introduces the DFT/FFT algorithms to compute signal amplitude spectrum and power spectrum; and uses the window function to reduce spectral leakage. Finally, the chapter describes the FFT algorithm and shows how to apply FFT it to estimate a speech spectrum.
17 citations