A novel algorithm for computing the 2D split-vector-radix FFT

  • Authors:

  • Hsuan-Yung Huang;Yu-Yun Lee;Pei-Chen Lo

  • Affiliations:

  • Department of Electrical and Control Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan, ROC;Department of Electrical and Control Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan, ROC;Department of Electrical and Control Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan, ROC

  • Venue:
  • Signal Processing
  • Year:
  • 2004

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Abstract

This paper presents a novel two-dimensional split-vector-radix fast-Fourier-transform (2D svr-FFT) algorithm. The modularizing feature of the 2D svr-FFT structure enables us to explore its characteristics by identifying the local structural property. Each local module is designated as a DFT (non-DFT) block if its output corresponds to DFT (non-DFT) values. The block attribute (DFT or non-DFT) directs the algorithm to construct the local module. We will show that the distribution of DFT blocks can be illustrated by the Sierpinski triangle--a class of fractals generated by IFS (iterated function system). The finding of the Sierpinski-triangle structural property enables us to actually implement the 2D svr-FFT algorithm. To the best of our knowledge, the 2D svr-FFT has never been realized in software. The computational efficiency of the proposed algorithm is considerably improved in comparison with that provided by Matlab.