*2.2. Two-Dimensional Fourier Transform*

The shape of dispersion curves can be determined by solving the dispersion equations, but also by processing the signals captured at the investigated structure. It is possible to measure the amplitudes of individual Lamb wave modes by using a 2-dimensional fast Fourier transform (2D-FFT) technique [21]. In this approach, the time-domain propagation signals recorded at the series of equally spaced positions along the propagation path are transformed and the data from the time–space plane are converted into the frequency–wavenumber plane according to the following expression:

$$Y(k,\omega) = \int\_{-\infty}^{+\infty} \int\_{-\infty}^{+\infty} \mathbf{u}(\mathbf{x},t)e^{-i(\mathbf{k}\cdot\mathbf{x}+\omega t)}d\mathbf{x}dt\tag{8}$$

where **u**(*x*,*t*) denotes the displacement of the surface.
