Systems Analysis of Discrete Two-Dimensional Signal Processing in Fourier Bases

  • Alexey V. PonomarevEmail author
Part of the Intelligent Systems Reference Library book series (ISRL, volume 184)


The problems of two-dimensional signals processing on the base of two-Dimensional Discrete Fourier Transform (2D DFT) are considered. A general definition and mathematical description of two-dimensional discrete signal is given. The algebraic form of 2D DFT is presented, the basic properties of 2D DFTs are briefly considered. The system analysis of the application of two-dimensional signal processing methods based on 2D DPF is carried out. The advantages and disadvantages of digital methods for discrete two-dimensional processing based on 2D DFT are considered. It is shown that the two-dimensional version of the discrete canonical decomposition of random signals proposed by Pugachev implies (by default) a modification of the standard cyclic two-dimensional correlation function of the original signal. A working hypothesis is proposed for solving the problem of discrete two-dimensional signal processing in the spatial-frequency domain.


Two-dimensional signal Two-dimensional discrete Fourier transform System analysis Canonical decomposition of random signals Cyclic two-dimensional correlation function Aperiodic two-dimensional correlation function 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Kalashnikov Izhevsk State Technical UniversityIzhevsk, Udmurt RepublicRussian Federation

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