A metric unified treatment of two-dimensional FFT

Abstract

A unification of fast algorithms for the discrete Fourier transform is discussed. A relationship is established with the coverings of sets of input data indices and their metric properties with respect to the families of non-Archimedean metrics. A n explicit analogy is given between the basic relations f o r the FFT-2 decomposition and the Stokes theorem on manifolds. Fast Fourier Transforms with reduced computational complexity are synrhesized.