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Abstract
A new expression for the Chernoff distance between two continuous-time stationary vector Gaussian processes that contain a common white noise component and have equal means is derived. The expression is given in terms of the spectral density matrices for large observation interval <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> . The expression is then used for deriving upper and lower bounds to the Bayes probability of error. Both bounds converge to zero exponentially in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> . It is also shown that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</tex> -divergence and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> -divergence can be easily evaluated in the frequency domain by differentiation of the Chernoff distance.
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