Spectral distance measures between continuous-time vector Gaussian processes (Corresp.)

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.