Estimating time delay and transfer function parameters using wideband transient signals

Experiments with a J15 moving-coil electrodynamic transducer are used to demonstrate the effectiveness of the output error method of identifying black-box transfer function models for underwater acoustic projectors and to introduce the signal energy centroid as a measure of the signal time of arrival for wideband signals transmitted through dispersive systems. The shift in the energy centroid or energy delay is shown to provide a direct and natural means of measuring an effective time delay between two signals that are not simply shifted replicas of each other. An expression is obtained relating the energy delay to the signal and system spectra. For a signal with a phase spectrum that is a linear function of frequency, the energy delay is shown to be an energy-density-weighted average of the system group delay. For a linear-phase signal and system, or for a distortion-free system, the energy delay reduces to simply the constant group delay of the system