Bilateral decomposition of a time function into laguerre series. Application to LTI system identification

This paper deals with the estimation of linear time invariant (LTI) systems using Laguerrien models. The Laguerre functions used in this paper are presented in their general form, i.e. using two exponential factors. The main contribution of this paper is the development of an algorithm which performs the decomposition of a signal into Laguerre series for negative as well as positive time domains. These two decompositions are then aggregated to form a unique bilateral expansion. The method is then used to decompose input and output signals defined for positive as well as negative time (the case of non zero initial conditions of the state process is considered) into their bilateral Laguerre expansions in order to compute the parameters of the transfer function of the system that needs to be identified.