Coefficient of coherence in the case of two vector random processes

A general method for estimating coherence and phase cross-spectra of vector random processes is described, and illustrated by examples. It is shown that the coherence matrix for two vector random processes with arbitrary dimension is the Hermitian matrix, which can be transformed to a diagonal form with real eigenvalues. For two-dimensional processes, the greater eigenvalue characterises the coherence between components of analysed vectors with respect to the direction of minimum noise variance, and the lesser value corresponds to the direction of maximum noise variance.