Abstract
Any Hermitian matrix, such as the spatial correlation matrix of measured data from an array of sensors at some frequency, can be represented as the sum of the dyads formed from its eigenvectors, weighted by the corresponding eigenvalues (the spectral decomposition of the matrix). Each term of this sum is of the form of the spatial correlation matrix due to a single source, received at the array with random amplitude, but fixed wave front (not necessarily planar). The spectral decomposition can thus be interpreted as analysis of the actual correlation matrix into components due to a number of (perhaps hypothetical) uncorrelated sources, with the appropriate complex delay factors and average powers displayed explicitly. In this note, we discuss this briefly, and illustrate with an example.
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