State-variable canonical forms for Prony's method

The parameters of a single-input single-output system (transfer function) are identified from the estimated parameters obtained using Prony's method to provide an exponential fit to the impulse-response data. The various relationships that exist between these two parameter sets are established by using state-variabie canonical forms. It is shown that the observability canonical form arises naturally from the algorithm that constitutes Prony's method. Finally, laboratory data involving the flow of a pesticide through an aquatic microcosm are used to illustrate the methods developed.