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.

When testing materials nondestructively with ultrasound, the grain scattering signal provides information that may be correlated to regional microstructure variation. Second and third-order autoregressive (AR) models are used to evaluate the spectral shift in grain signals by utilizing features such as resonating frequency, maximum energy frequency, or AR coefficients. Then, Euclidean distance, based on these features, is applied to classify grain scattering characteristics. Using both computer simulated data and experimental results, the probability of correct classification is found to be about 75% for the second-order AR model and 88% for the third-order AR model, when the conditions are such that the expected shift between the center frequency of echoes is less than 4%. This implies that, by increasing the order of the AR model, the frequency information extracted from the random signal is increased, which can result in obtaining a better classification.

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