Lensless display of phase-space functions for 1-D signals

A coherent lensless processor for displaying a 1-D Fourier transform is proposed. It is shown that under appropriate conditions the diffraction produced by certain 2-D objects can be approximated to a 1-D Fourier transformer. In particular we show that this processor is useful in order to display phase-space functions of 1-D signals, which involves in their definitions a 1-D Fourier transform, like the Wigner distribution function, ambiguity function, and local spectrum.