On the Interpolation of Ultrasonic Guided Wave Signals

The application of ultrasonic guided wave methods to both nondestructive evaluation (NDE) and structural health monitoring (SHM) is becoming more prevalent as techniques to handle their multi-modal and dispersive nature are developed. There are several applications where it would be not only convenient but perhaps essential to interpolate arrays of measured guided wave signals. One application is that of linear spatial arrays acting as receivers, where it may be useful to interpolate signals in between array elements. Another application is interpolation of signals acquired as a function of a non-spatial variable such as temperature or applied load; this situation arises in SHM applications where it is desired to construct a baseline that is well-matched to the signal of interest. This problem is closely related to that of time domain up-sampling whereby signals are resampled at a higher rate, which can readily be performed using sinc interpolation when the Nyquist criterion is satisfied. In the spatial domain, there is an analogous spatial Nyquist criterion, and if it is satisfied, spatial signals can be similarly up-sampled. In this paper we derive a Nyquist criterion for sinc interpolation in the temperature domain. Examples are shown of sinc, linear and spline interpolation algorithms, and the efficacy of each is evaluated on both simulated and experimental data. Concluding remarks are made regarding both the usefulness and limitations of guided wave signal interpolation.