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Spectral distance measures between continuous-time vector Gaussian processes

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 T . The expression is then used for deriving upper and lower bounds to the Bayes probability of error. Both bounds converge to zero exponentially in T . It is also shown that the I -divergence and J -divergence can be easily evaluated in the frequency domain by differentiation of the Chernoff distance.