Abstract

One-dimensional signals have complementary attributes, their space and spatial frequency properties. Recently, another signal representation was introduced in optics, the Wigner distribution (WD) function, which allows the simultaneous display of the two attributes of a 1-D signal. In this paper optical implementation of a generalized space–spatial frequency (GSF) function is discussed. Special cases of the GSF representations are the WD, the radar ambiguity function (AF), the energy distribution function, the various pseudo-WD functions, the spectrogram, the local frequency and the local Doppler frequency spectrum. The GSF representation allows the simultaneous filtering of both the spatial and the spatial frequency content of a 1-D signal. The 2-D filtering of a 1-D signal allows sidelobe reduction of the WD and AF of quasi-periodic 1-D signals, display of the instantaneous spatial frequency content of a 1-D signal, space–spatial frequency excision of a desired portion of a 1-D signal as well as the usual matched filter detection. Experimental results using coherent space-integrating techniques for the realization of different GSF are presented.

© 1982 Optical Society of America

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