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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.

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The propagation speed of a shock or detonation wave in a shock or detonation tube is usually determined by a time-of-flight method by dividing the distance between two transducers with the propagation time of the disturbance signal. Some arbitrariness is inherent in determining the propagation time by this method. A new method based on Haar and Morlet wavelet transforms is reported. The method was tested against a step and a decaying spike with added noise, which are representative of shock and detonation waves. The wavelet methods can be applied to the step discontinuity provided that the SNR ratio is good. The wavelet methods worked very well for the decaying spike in the presence of noise.