Two-Dimensional Discrete Fourier Transform with Variable Parameter in the Spatial-Frequency Domain

The practice of using Fourier - processing of finite two-dimensional signals (including images), having confirmed its effectiveness, revealed a number of negative effects inherent in it. The purpose of this paper is to develop new discrete Fourier transforms for efficient and effective processing of two-dimensional signals. We have proposed a new method for splitting a rectangular discrete Fourier transform matrix into square matrices. Methods are based on the application of the modulus comparability relation to order the rows (columns) of the Fourier matrix. New discrete Fourier transforms with variable parameters were developed. The proposed discrete Fourier transforms with variable parameters are a generalization of the classical discrete Fourier transform. The developed discrete Fourier transforms with variable parameters can significantly reduce the cost of Fourier - processing of two-dimensional signals (including images), padded with zeros.