Fast computation of RBF coefficients using FFT

  • Authors:
  • Yoshinori Abe;Youji Iiguni

  • Affiliations:
  • Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan;Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka, Japan

  • Venue:
  • Signal Processing - Special section: Distributed source coding
  • Year:
  • 2006

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Abstract

A fast method of computing radial basis function (RBF) coefficients for uniformly sampled data with the fast Fourier transform (FFT) is proposed. A periodic RBF network which is characterized by a set of periodic RBF coefficients is first introduced. The periodic RBF coefficients are then computed by using the FFT in O(N log N) computation time, where N is the number of observed data. The original RBF coefficients are approximately computed from the periodic RBF coefficients by using a sparse matrix transform in O(N) computation time. The approximation accuracy is theoretically investigated. The method for 1-D inputs is extended to 2-D by a successive computation of 1-D RBF coefficients.