Analysis of homomorphic processing for ultrasonic grain signal characterization

A model for the grain signal is presented, which includes the effect of frequency-dependent scattering and attenuation. This model predicts that the expected frequency increases with scattering and decreases with attenuation. Homomorphic processing was used for spectral smoothing, and the selection of parameters for optimal performance was examined. Experimental results are presented that show both the upward shift in the expected frequency with grain boundary scattering and the downward shift with attenuation. Furthermore, it is shown that the expected frequency shift can be correlated with the grain size of the material. It is important to point out that the quantitative relationship between the average grain size and the expected frequency shift (either upward or downward) is dependent on the type of material, the quality of grain boundaries, and the characteristics of the measuring instruments.