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Detection of Wave Propagation by Nonstationary Cross-Correlation and Cross-Spectral Density Phase

The accurate determination of the speed of a propagating disturbance is important for a number of applications. A nonstationary cross-spectral density phase (NCSDP) technique was developed to provide a statistical estimate of the propagation time of sharp discontinuities such as steps or spikes that model shock or detonation waves. The uncertainty of the phase estimate is dependent on the coherence between the signals. For discrete implementation of the NCSDP technique, a “weighted-resetting-unwrap” of the phase angle was proposed to discard values of the coherence below a threshold value, that is, only the unwrapped phase angle above the threshold was accepted. In addition, an envelop function was used which improved the technique. The technique was found to be unsuitable for step disturbances but was more effective in estimating the time delay with a small standard deviation if the sharp disturbance also showed a rapid decay.