Laplace spectrum for exponential decomposition and pole-zero estimation

A novel Laplace transform power spectrum is proposed as a basic tool for complex-exponential decomposition of finite-duration continuous functions. The weighted spectrum leads to a direct decomposition in terms of exponential damping function content in addition to the usual decomposition in terms of sinusoidal circular content produced by Fourier and Laplace transforms. The weighting results in a two-dimensional spectral peak on the Laplace s-plane identifying the exponential and frequency content of finite-duration functions. An algorithm for two-dimensional generalised spectral analysis of finite duration functions is described. It is shown that the proposed spectral weighting eliminates the exponential divergence of spectra of usual transforms which masks poles along one dimension of the complex plane. As an application, an algorithm for mathematical modelling pole-zero estimation through a direct two-dimensional localisation of pole-zero peaks of weighted spectra is described