SPECTRAL METHODS FOR THE SOLUTION OF LINEAR DESCRIPTOR SYSTEMS USING FOURIER FUNCTIONS

In this paper a spectral method using orthogonal periodic basis functi ons for the analysis of linear time invariant descriptor systems is di scussed, and the case of the trigonometric Fourier functions is invest igated in detail. The method is shown to be convergent, in the distrib utional sense. However, for any finite number of basis functions, the periodicity induced by the chosen basis can give rise to spurious impu lsive components in the computed system response, even in the case of correct initial conditions.