Vector coding algorithms for multidimensional discrete Fourier transform

Authors:
Zhaodou Chen;Lijing Zhang
Affiliations:
School of Information Engineering, China University of Geosciences (Beijing), Beijing 100083, China;Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

A new fast algorithm is presented for the multidimensional discrete Fourier transform (DFT). This algorithm is derived using an interesting technique called ''vector coding'' (VC), and we call it the vector-coding fast Fourier transform (VC-FFT) algorithm. Since the VC-FFT is an extension of the Cooley-Tukey algorithm from 1-D to multidimensional form, the structure of the program is as simple as the Cooley-Tukey fast Fourier transform (FFT). The new algorithm significantly reduces the number of multiplications and recursive stages. The VC-FFT therefore comprehensively reduces the complexity of the algorithm as compared with other current multidimensional DFT algorithms.