Complex-Conjugate Symmetry of Coefficients of Two-Dimensional Discrete Fourier Transform with Variable Parameters of Real Signals

Abstract

Methods and algorithms for digital one-dimensional and two-dimensional Fourier processing have the widest applications in solving a wide range of practical problems in many areas of scientific research. The paper gives a generalization of standard discrete Fourier transform in the form of parametric discrete Fourier transform, and considers the theory of its application. The article considers new discrete two-dimensional Fourier transform which is discrete two-dimensional Fourier transform with variable parameters, which, being a generalization of standard two-dimensional discrete Fourier transform, has a number of advantages over the standard one. Due to the widespread use of real signals in practice, the paper investigates the properties of the complex-conjugate symmetry of the coefficients of two-dimensional discrete Fourier transform with variable parameters for this class of signals. The concept of cross-complex-conjugate symmetry of the coefficients of two-dimensional discrete Fourier transform with variable parameters for real signals is introduced. The properties of the cross-complex-conjugate symmetry of the coefficients of two-dimensional discrete Fourier transform with variable parameters for real signals are confirmed by the results of mathematical modeling. Methods and algorithms for fast computation of discrete Fourier transform with variable parameters of real signals for various combinations of variable parameters have been developed.