DocumentCode :
937646
Title :
Solution of an integral equation occurring in the theories of prediction and detection
Author :
Miller, K.S. ; Zadeh, L.A.
Volume :
2
Issue :
2
fYear :
1956
fDate :
6/1/1956 12:00:00 AM
Firstpage :
72
Lastpage :
75
Abstract :
In many of the theories of prediction and detection developed during the past decade, one encounters linear integral equations which can be subsumed under the general form \\int_a^b R(t, \\tau ) x(\\tau ) d\\tau = f(t), a \\underline\\leq t \\underline\\leq b . This equation includes as special cases the Wiener-Hopf equation and the modified Wiener-Hopf equation \\int_0^T R(\\mid t - \\tau \\mid ) x(\\tau ) d\\tau = f(t), 0 \\underline\\leq t \\underline\\leq T . The type of kernel considered in this note occurs when the noise can be regarded as the result of operating on white noise with a succession of not necessarily time-invariant linear differential and inverse-differential operators. For this type of noise, which is essentially a generalization of the stationary noise with a rational spectral density function, it is shown that the solution of the integral equation can be expressed in terms of solution of a certain linear differential equation with variable coefficients.
Keywords :
Integral equations; Prediction methods; Signal detection; Density functional theory; Differential equations; Filters; Gaussian noise; Integral equations; Kernel; Maximum likelihood detection; Maximum likelihood estimation; Signal detection; Signal to noise ratio; Stochastic processes; White noise;
fLanguage :
English
Journal_Title :
Information Theory, IRE Transactions on
Publisher :
ieee
ISSN :
0096-1000
Type :
jour
DOI :
10.1109/TIT.1956.1056787
Filename :
1056787
Link To Document :
بازگشت