We introduce a novel approach for measuring the frequency spectrum of Lamb waves and, subsequently, for obtaining the thickness and the bulk wave velocities of isotropic, homogeneous plates. It is based on Fourier transforming a set of spatial and temporal samples of the acoustic displacement but, in contrast to the traditional approach that employs dense temporal sampling and a reduced set of spatial sampling locations, our data set is a sequence of 2-D high-resolution maps of the instantaneous out-of-plane displacement obtained with TV holography. We have devised three variants to obtain a set of points of the wavenumber-frequency space, based, respectively, on the spatial (1-D or 2-D) and on the spatio-temporal (3-D) Fourier transforms. The whole process to obtain these points can be easily automated and substantial time savings can be achieved, compared with other full-field techniques that require human intervention or with pointwise scanned probes. Experimental demonstration of the three variants with quasimonochromatic multimode Lamb waves in aluminum plates is presented. The characteristic parameters of the plates are calculated by fitting the theoretical model to the experimental points of the frequency spectrum. The analysis of the uncertainties shows that the accuracy of the method is only slightly lower than the accuracy of a previously reported method based on measuring the wavelength of single-modes, for which the data acquisition procedure is much slower.