A theorem on cross correlation between noisy channels

Author

Keilson, J. ; Mermin, N.D. ; Bello, P.

Volume

Issue

fYear

1959

fDate

6/1/1959 12:00:00 AM

Firstpage

Lastpage

Abstract

Two channels carry noise waveforms, $N_0 (t) + N_1 ( t)$ and $N_0 (t) + N_2 (t)$ , where $N_0 (t)$ is a common narrow-band Gaussian noise and $N_1 (t)$ and $N_2 (t)$ are independent narrow-band Gaussian noises associated with each channel. The outputs of each channel are sent through detectors whose outputs, $F(x, y)$ , are identical homogeneous functions of the components, $x$ and $y$ , of their inputs $N$ , where $N(t) = x(t) \\cos \\omega _0 t + y(t) \\sin \\omega _0 t$ . Let $R_{12}(\\tau )$ be the normalized cross-correlation function of the two detector outputs. It is shown that to determine $R_{12}(\\tau )$ it suffices to know the normalized auto-correlation function $R_0(\\tau )$ of the output of a single such detector when the input is $N_0(t)$ ; i.e., if $R_0(\\tau ) = G(\\sigma _0^2, p(\\tau ))$ where $p(\\tau )$ and $\\sigma _0$ are the normalized auto-correlation function and rms of either component of $N_0$ , then it is shown that $R_{12}(\\tau ) = G(\\sigma _0^2, Z_{\\rho}(\\tau ))$ where $Z = [{1 + (\\sigma _1^2/\\sigma _0^2)} {(1 + (\\sigma _2^2/\\sigma _0^2)}]^{-frac{1}{2}}$ .

Keywords

Correlation functions; Autocorrelation; Envelope detectors; Gaussian noise; Gaussian processes; Information theory; Narrowband; Phase detection; TV; White noise;

fLanguage

English

Journal_Title

Information Theory, IRE Transactions on

Publisher

ieee

ISSN

0096-1000

Type

jour

DOI

10.1109/TIT.1959.1057496

Filename

1057496

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=944849