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• [P484] Elliptic Discrete Fourier Transforms of Type II
  Author(s): Artyom M. Grigoryan
  
  

  Abstract
  This paper presents a novel concept of the N-point elliptic DFT of type II (EDFT-II), by considering and generalizing the N-point DFT in the real space R^{2N}. In the definition of such Fourier transform, the block-wise representation of the matrix of the DFT is reserved and the Givens transformations for multiplication by twiddle coefficients are substituted by other basic transformations. The elliptic transformations are defined by different Nth roots of the unit matrix 2x2, whose groups of motion move the point (1,0) around ellipses. The elliptic DFTs of type II are parameterized by two vector-parameters and exist for any order N and they differ from the class of elliptic DFT of type I with the basic transformations defined by the elliptic matrix cos(phi)I+sin(phi)R, where R is such a matrix that R^2=-I and I is identity matrix 2x2. Examples of application of the proposed N-block EDFT-II in signal and image processing are given.

  
   

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