Time-frequency signal analysis of hydrophone data

The acoustic spectrum of a transiting aircraft, when received by a hydrophone located beneath the sea surface, changes with time due to the acoustical Doppler effect. The traditional method for analysing signals whose frequency content changes with time is the short-time Fourier transform that selects only a short segment of the signal (or window of data) for spectral analysis at any one time. The short-time Fourier transform requires the frequency content of the signal to be stationary during the analysis window, otherwise the frequency information will be smeared by the transformation. Recently, joint time-frequency distributions, which highlight the temporal localisation of a signal's spectral components, have been used to analyse nonstationary signals whose spectra are time dependent. In this paper, the short-time Fourier transform and the Wigner-Ville time-frequency distribution are applied to time-series data from a hydrophone so that the instantaneous frequency of the propeller blade rate of a turbo-prop aircraft can be estimated at short time intervals during the aircraft's transit over the hydrophone. The variation with time of the estimates of the Doppler-shifted blade rate is then compared with the corresponding temporal variation predicted using a model that assumes the sound propagates from the airborne acoustic source to the subsurface receiver through two distinct isospeed media (air and water) separated by a plane boundary (the air-sea interface). The results for five transits are presented in which the altitude of the aircraft ranged from 350 to 6050 ft with the speed of the aircraft varying from 232 to 245 kn.