Wigner distribution and ambiguity function

Abstract

The Wigner phase space distribution and the Woodward radar ambiguity function have each been optically realized in idealized situations. The realistic performance will be assessed under simulated noise and clutter. A general cross Wigner distribution and cross ambiguity function are also compared as to their advantage in signal analysis. The cross Wigner distribution is a general convolution of non‐zero frequency while the cross ambiguity function is a general correlation of non‐zero frequency. The former is commutative while the latter is not. The significance of this difference is discussed. While the ambiguity function is generally complex, the Wigner distribution is real but not always positive. Both are known to be intermediate signals and are related through a double Fourier transform. However, optical equivalence of one from the other has not been demonstrated. Bartelt et al1 have only produced the even part of the signal whose Wigner distribution is jpositive. Marks et al2 have presented in the noise‐free case the modulus of the ambiguity function, which is known as the ambiguity surface in the radar community. The present extension with noise and clutter provides a better understanding of the optimum condition for signal to noise ratio. Such a comparison study, which takes into account both knowledge of quantum mechanical symmetry and practical experience of radar clutter and noise, turns out to be fruitful.