General Concepts

Interesting processing concepts are discussed quite often in guided wave studies. In guided wave analysis, it is often useful to think on a frequency basis rather than to employ more common time domain thinking. As a result, Fourier transform analysis is commonplace. An analytic envelope for a Hilbert transform is also useful. The short time Fourier transform (STFFT) can also provide significant insight into the studies of guided wave response functions encountered in different situations. Physical insight into a resulting image of a spectrogram and its relationship to a group velocity dispersion curve along with the wavelet transform and its ability to see when certain frequency packets arrives as a function of time, as well as its relationship to a group velocity dispersion curve. On the other hand, the 2-D Fourier transform (2DFFT) relates to portions of a phase velocity dispersion curve. Quite often, the partial images generated by these transform techniques can provide us with an indication of damage in a structure by shifting and other indicators.

This appendix gives an overview of some of these transform techniques that can also be used as a basis for extracting features that provide insight into important characteristics of guided waves. In particular, they provide data for constructing portions of the relevant dispersion curves, identifying the modes that are actually propagating, and providing a physical explanation of certain aspects of ultrasonic guided wave propagation.