21 January 1985 Scale-Invariant Wigner Distribution And Ambiguity Functions
Author Affiliations +
Proceedings Volume 0519, Analog Optical Processing and Computing; (1985) https://doi.org/10.1117/12.945198
Event: 1984 Cambridge Symposium, 1984, Cambridge, United States
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.
© (1985) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
G. Eichmann, N. M. Marinovic, "Scale-Invariant Wigner Distribution And Ambiguity Functions", Proc. SPIE 0519, Analog Optical Processing and Computing, (21 January 1985); doi: 10.1117/12.945198; https://doi.org/10.1117/12.945198


Generalized classical and quantum signal theories
Proceedings of SPIE (May 25 2005)
Invertible time-frequency representations
Proceedings of SPIE (October 02 1998)
Optical And Analog Electronic Signal Processing
Proceedings of SPIE (December 28 1977)
Accurate Numerical Computation By Optical Convolution
Proceedings of SPIE (August 22 1980)

Back to Top