Elliptic discrete fourier transforms of type II

This paper presents a novel concept of the iV-point elliptic DFT of type II (EDFT-II), by considering and generalizing the iV-point DFT in the real space R^2N. In the definition of such Fourier transformation, the block-wise representation of the matrix of the DFT is reserved and the Givens transformations for multiplication by the twiddle coefficients are substituted by other basic transformations. The elliptic transformations are defined by different iVth roots of the identity matrix 2 × 2, whose groups of motion move the point (1, 0) around ellipses. The elliptic DFTs of type II are parameterized by two vector-parameters, exist for any order N, and differ from the class of elliptic DFT of type I whose basic transformations are defined by the elliptic matrix cos(¿)I + sin(¿)R, where R is such a matrix that R² = -I and I is the identity matrix 2 × 2. Examples of application of the proposed iV-block EDFT-II in signal and image processing are given.