Frequency-domain characteristic analysis of PCNN

The pulse-coupled neural network (PCNN) is widely used in digital image processing. Although existing studies mainly analyze the network from the time-domain perspective, there are still some limitations in revealing the characteristics of network. In this paper, from the iterative equations of PCNN, the expressions for the firing time and firing interval of neuron are given. Spectrum for the dynamic threshold subsystem and firing subsystem of PCNN is given by using the Z-transform and the discrete Fourier transform, and the effects of different parameters aE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a_{E}$$\end{document}, VE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{E}$$\end{document} and K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K$$\end{document} on the frequency-domain characteristics of the two subsystems are analyzed. The edge detection phenomenon exhibited by the iterative output of the PCNN is explained by analyzing the effect of the neighbor coupling state on the firing time and interval. Finally, the correctness of the analysis is validated by simulation experiments, which provides a new idea for the further study into the characteristics of PCNN.