Effect of signal-processing parameters on phase velocity uncertainty

Quantification of signal-processing effects is required for an accurate determination (less than 1% uncertainty) of the absolute phase velocity, particularly when Fourier techniques are used. The velocity is calculated by using the travel time determined from the phase differences between the spectra of two successive signals. In practice, the frequency spectra are estimated using Discrete Fourier Transforms (DFT). However, using the DFT requires sampling and windowing of the received waveforms. We present a comprehensive and self-consistent method of analysis that allows one to derive a relation for the uncertainty of the phase velocity as a function of the sampling-parameters, window-shape, noise-variance and travel-time. We compare the results of our method with results for a pulse-echo, 5 MHz measurement of the velocity on a 25.4 mm thick steel specimen. For a signal-to-noise ratio of 40 dB, the theoretically predicted and experimentally determined imprecisions are 0.07% and 0.05% respectively