ABSTRACT
This chapter devises a procedure with the goal of checking the internal consistency of spectral analysis within the PLA. For this purpose, it adapts the Longman and Sharir method which has originally been designed for the Laplace inversion of rational response functions. Exact reconstruction of the set of the initial data {cn} is essential for a retrospective validation of the performed spectral analysis. Such a reconstruction should yield accurate values for the quantities {cn} in an efficient and numerically stable way. The chapter analyses a computational algorithm of this type. It demonstrates the derivation of the algorithm for the exact reconstruction of the input data that are auto-correlation functions or time signal points {Cn} = {cn}, without having to compute the set {uk, dk} of the eigenvalues and residues.
