On a Direct Approach for the Solution of Linear Space-Invariant 2-D Differential Convolution Models
2-D differential convolution operators in a rectangular discrete domain are modelled as linear differential matrix equations of the form Х(t) = Σ AjX(t)Bi + F(t), where the coefficient matrices Ai ∈ IR(MxM),Bi ∈ IR(NxN) and F(t) ∈ IR(MxN) is a piecewise continuous function matrix of t. Under some periodicity assumptions an analytical solution method is presented making use of the 2-D discrete Fourier transform (DFT). For most general problems an iterative computational method founded in the Peano-Baker series is proposed.
KeywordsDiscrete Fourier Transform Circulant Matrice Inverse Discrete Fourier Transform Differential Matrix Equation Convolution Process
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