We investigate the recognition of fingerprints from the Fourier spectrum. The inherent properties of fingerprints allow a feature extraction and data reduction in the spatial frequency domain. The Fourier representation allows fingerprints to be distinguished from a small and spatially well-defined area. This suggests various schemes to detect the significant information in order to optimize the trade-off between sensitivity and robustness. We show illustrative results which confirm the usefulness of this approach. In addition, the classification of fingerprints from their plane wave spectra allows the design of compact systems, where the Fourier transformation is performed optically, while detection and post-processing is done by electronics. This provides the advantage that both optics and electronics are used in an optimum way to minimize the physical size of the system, as well as the computational load to interpret the detected signal.