Cart (Loading....) | Create Account
Close category search window

A systematic approach to a class of problems in the theory of noise and other random phenomena--III: Examples

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)

The method of Part I is applied to the problem of finding the characteristic function for the probability distribution ofint_0^t sum_{jk} x_j (tau) K_{jl}(tau)x_l(tau) dtau, wherex_j(tau)denotes thejth component of a stationary n-dimensional Markoffian Gaussian process. The problem is reduced to the problem of solving2nfirst-order linear differential equations with initial conditions only. For the case of constantK, the explicit solution is given in terms of the eigenvalues and the first2n - 1powers of a constant2n times 2nmatrix. For the case of a symmetric correlation matrix which commutes withK, the problem is reduced to the one-dimensional case treated in Part II. For the caseK_{ij}(t) = delta_{il} delta_{jl} e^{-t}, where the functional represents the output of a receiver consisting of a lumped circuit amplifier, a quadratic detector, and a single-stage amplifier, the solution has been obtained in a form which is more explicit than that provided by the earlier methods.

Published in:

Information Theory, IRE Transactions on  (Volume:4 ,  Issue: 1 )

Date of Publication:

March 1958

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.