Theory of optimal M-ary filtering of signals on a background of correlated noise

Consideration is given to the identification of signals according to the Neumann-Pearson criterion on a background of additive normal noise by means of linear discrete M-ary filters. It is shown that the impulse response of the optimal filter depends on the form of the signal and the M-ary correlation function of the noise. The noise immunity of conventional and M-ary optimal linear filters is examined for the case of additive normal correlated noise.