Multivariate-multidimensional Rihaczek spectra and associated canonical correlations

Harmonizable processes constitute an important class of non-stationary stochastic processes. In this paper we study the important extension to multivariate harmonizable random fields. We derive the multivariate-multidimensional Rihaczek spectrum and show that it determines a complex time-frequency varying Wiener filter for approximating a multivariate random field from its infinitesimal Fourier generator. We derive the time-frequency coherence function, and generalize it to canonical correlations between a time domain subspace and a frequency domain subspace. We show how to construct estimators, and we finally demonstrate the theoretical concepts by the analysis of synthetic data.