Linear Discriminant Functions for Stationary Time Series

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Abstract
Certain spectral approximations are applied to the problem of discriminating between two normal processes by linear filtering. Limiting values for the (1) Kullback-Leibler discrimination information rate, (2) J-divergence rate and (3) detection probability are expressed in terms of the spectral densities of the two populations and the Fourier-Stieltjes transform of the mean difference between them. Spectral approximations to (1), (2) and (3), convenient for computing, are shown to have the same limits. Linear discriminant filters maximizing (1), (2) and (3) are approximated by the same methods and applied to seismic records from selected earthquakes and nuclear explosions.

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