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Proceedings Paper

Scale-Invariant Wigner Distribution And Ambiguity Functions
Author(s): G. Eichmann; N. M. Marinovic
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Paper Abstract

The Wigner distribution (WD) function is a two-dimensional representation that displays the space and spatial frequency content of a one-dimensional signal. Its two-dimensional Fourier transform, the radar ambiguity function, displays the space and spatial frequency shifts of the same signal. The WD has the property that a space or spatial frequency shift of the signal leads to a corresponding shift of the Wigner distribution function. This represents a translation invariance of the WD, a property that is useful for impulse response characterization of a space-invariant system. Similarly, if one signal is shifted with respect to the other, magnitude of their cross-ambiguity function is shifted by the same amount. There are many optical systems that are space-variant. A particular space-variant system, encountered in many imaging applications, is the so-called scale-invariant system. In this paper, scale-invariant Wigner distribution and ambiguity functions are defined. These new functions represent local scale-frequency spectrum of the signal, and scale correlation in space and scale frequency. Properties of these functions are described and the differences and similarities to translation-invariant WD and ambiguity function are pointed out. Potential applications and analog optical implementations of these functions aie also discussed.

Paper Details

Date Published: 21 January 1985
PDF: 7 pages
Proc. SPIE 0519, Analog Optical Processing and Computing, (21 January 1985); doi: 10.1117/12.945198
Show Author Affiliations
G. Eichmann, City College of the City University of New York (United States)
N. M. Marinovic, Philips Laboratories (United States)


Published in SPIE Proceedings Vol. 0519:
Analog Optical Processing and Computing
H. John Caulfield, Editor(s)

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