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Abstract

Embodiments described herein describe the construction of frequency domain estimates of generalized power density and the filters that can be constructed from those estimates. Using the concept of the Stokes vector representation of the spectral matrix in an M-dimensional vector space, a generalization of the process in which the spectral matrix may be represented by a set of trace-orthogonal matrices that are based upon a particular signal state can be produced. One aspect of the process is as follows: given a particular signal, represented as by a state vector in the space, a complete, orthonormal set of vectors can be produced that includes the signal of interest. Then, a generalized set of matrices is constructed, based upon the developed vectors, that are trace-orthogonal and which serve as a basis set for the expansion of the spectral matrix. The coefficients of this expansion form a generalized Stokes vector that represents the power in the spectral matrix associated with the various state vectors. Filters that serve to extract or suppress information about a particular state may then be constructed using the components of the generalized Stokes vectors. The effectiveness of an embodiment this filter is demonstrated using acoustic data from a microphone array.

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First Claim