Journal ArticleDOI
On a moment theorem for complex Gaussian processes
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A general theorem is provided for the moments of a complex Gaussian video process that states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.Abstract:
A general theorem is provided for the moments of a complex Gaussian video process. This theorem is analogous to the well-known property of the multivariate normal distribution for real variables, which states that an n th order central product moment is zero if n is odd and is equal to a sum of products of covariances when n is even.read more
Citations
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ReportDOI
Statistical properties of laser sparkle patterns
TL;DR: In this article, the first order statistics of the observed electric-field strength, the observed light intensity, and observed light phase are examined, and the autocorrelation functions of the complex field and intensity processes are investigated, and that of the electric field is found to be proportional to the Fourier transform of the light intensity distribution incident on the scattering surface.
Book ChapterDOI
Statistical Properties of Laser Speckle Patterns
TL;DR: In this article, the first-order statistics of the complex amplitude, intensity and phase of speckle are derived for a free-space propagation geometry and for an imaging geometry.
Journal ArticleDOI
Proper complex random processes with applications to information theory
F.D. Neeser,J.L. Massey +1 more
TL;DR: The covariance of complex random variables and processes, when defined consistently with the corresponding notion for real random variables, is shown to be determined by the usual complex covariance together with a quantity called the pseudo-covariance.
Journal ArticleDOI
Coherence Properties of Optical Fields
Leonard Mandel,Emil Wolf +1 more
TL;DR: In this paper, a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum, is presented, based on both the classical and quantum theories.
Journal ArticleDOI
Theory of Adaptive Radar
L.E. Brennan,L.S. Reed +1 more
TL;DR: In this paper, the authors review the principles of adaptive radar in which both the spatial (antenna pattern) and temporal (Doppler filter) responses of the system are controlled adaptively.
References
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Journal ArticleDOI
Mathematical analysis of random noise
TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Journal ArticleDOI
The Detection of Radar Echoes in Noise. I
Journal ArticleDOI
Complex processes for envelopes of normal noise
TL;DR: The paper presents a brief exposition of the technique of complex normal random variables as utilized in the study of the envelopes of Gaussian noise processes, with central concept the pre-envelope z( ) of a real normal process.