Use of rectangular vandermonde matrix decomposition to resolve damped sinusoidal oscillation components

Abstract

Signals that are sums of decaying sinusoids arise frequently in passive and active sonar applications, both as spontaneous acoustic transients and as echoes from elastic objects. When the oscillations are highly damped, identification of component frequencies and damping factors is more amenable to least‐squares Prony analysis than to Fourier analysis, and is particularly suited to a related technique that we call “rectangular Vandermonde matrix decomposition.” Our results indicate that the Vandermonde method is robust in the presence of noise, but not in the presence of distortions created by ideal bandpass filters. On the other hand, analysis of simulated replica‐correlated echoes of FM pulses bounced off an object having a pair of heavily damped resonances give different results. Surprisingly, the Vandermonde method identified the resonant frequencies even without replica correlation, despite the fact that the analyzed waveform looked not at all like a sum of decaying sinusoids. [Work supported by the ONR.]