The complete characterization of a multiple sinusoid signal

Many problems of practical import can be formulated mathematically as problems in signal identification, where the signal is modeled as a finite number of discrete sinusoidal components which are additively combined and corrupted by an additive zero mean white noise source. It is desired to identify the parameters which characterize the signal; that is, the power (or amplitude), phase, and frequency of each of the sinusoids, and the noise power. A recently developed technique which shows much promise in its ability to estimate parameters of such a signal is Pisarenko´s Harmonic Decomposition (PHD). Given such a signal, PHD will estimate the number of sinusoids present, the powers of each of the sinusoids, and the power of the noise. What is missing from a complete characterization of the signal is an estimate of the phases of the sinusoids. The goal of our effort has been to extend the PHD to yield phase information and thus to give the complete characterization of the signal.