2-D Laplace-Z Transformation

Based on recent results for 2-D continuous-discrete systems, this paper develops 2-D Laplace-z transform, which can be used to analyze 2-D continuous-discrete signals and system in Laplace-z hybrid domain. Current 1-D Laplace transformation and z transform can be combined into the new 2-D s-z transform. However, 2-D s-z transformation is not a simple extension of 1D transform, in 2-D case, we need consider the 2-D boundary conditions which don’t occur in 1-D case. The hybrid 2-D definitions and theorems are given in the paper. To verify the results of this paper, we also derived a numerical inverse 2-D Laplace-z transform, applying it to show the 2-D pulse response of a stable 2-D continuous-discrete system.