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Author Kadota, T.T.
Source IEEE Xplore Digital Library
Content type Text
Publisher Institute of Electrical and Electronics Engineers, Inc. (IEEE)
File Format PDF
Copyright Year ©1970
Language English
Subject Domain (in DDC) Technology ♦ Engineering & allied operations ♦ Other branches of engineering
Subject Keyword Gaussian noise ♦ Signal processing ♦ White noise ♦ Telephony ♦ Laboratories ♦ Integral equations ♦ Random variables ♦ Convergence
Abstract Through a purely formal manipulation, one can show that the optimum detection of a zero-mean Gaussian signal in "white Gaussian noise" is achieved by the following decision rule: the signal is present if (x,Hx) ¿ c, the signal is absent otherwise, where x is the observable waveform, H is a solution of an integral equation H + SH = S, with S(t,s) being the signal covariance, and c is a preset threshold. Since the white Gaussian noise is a mathematical fiction, neither the quadratic form (x,Hx) nor the whole detection problem has any meaning. With the use of the Wiener process, however, we rigorously show that the above decision rule can be regarded as an approximate solution to a well-defined realistic optimum detection problem. By comparing with the exact solution, we give a qualitative argument that it is a good approximation.
Description Author affiliation: Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey (Kadota, T.T.)
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research ♦ Reading
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1970-12-07
Publisher Place USA
Rights Holder Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Size (in Bytes) 435.74 kB
Page Count 1
Starting Page 71
Ending Page 71


Source: IEEE Xplore Digital Library