Inversion and Simulation of Two Models of the Wave Equation

M. Sarhan (USA)

Keywords

System Inverse, Fourier Series, Distributed Parameter Systems, Transfer Function, The Wave Equation and LaplaceTransform

Abstract

Inthis paper, we present the lossless and the lossy models of the wave equation in one dimension with a boundary input and distributed output. With a very simple expansion, we derive the transfer function of each system using Fourier series analysis. Truncating Fourier series in each case, gives an approximate system representing the input - output relation. We follow by finding the truncated inverse system in each case. We derive the error bound due to approximation then present examples to show the accuracy of the approximation.

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