APPROXIMATION AND DECOMPOSITION OF FUNCTIONS AND DISTRIBUTIONS BASED ON PRONY METHOD
Doctor of Philosophy thesis
This dissertation presents certain extensions and applications of the Prony method both in real and complex domains. First, a recursive algorithm for the conventional (time domain) Prony method is developed for finding the optimal solution under both no noise and additive white noise conditions. The technique developed allows the determination of the order of the system model. The result is applicable to the linear system model reduction problem. Next, the Prony method in the frequency domain is investigated. A superposition (mixture) of one or more differently delayed versions of a given signal is analyzed. Even though the data used is in the complex domain, the technique does the curve fitting in the real domain. The method is then applied to the problem of identification and recognition of short pulse radar signatures. It performs well even under low signal-to-noise ratio conditions. The complex domain Prony method is also applicable to the problem of the decomposition of a superposition of shifted probability density functions (pdf's), especially the Cauchy pdf's and the Gaussian pdf's. The method is used to obtain the means and the coefficients in the individual pdf's in the mixture. The variances are obtained in a second stage. The technique is then applied to a communication signal detection problem. Simulation examples yield satisfactory results.
Engineering, Electronics and Electrical