Exploiting multiple shift invariances in harmonic retrieval

A novel algorithm for estimating multi-dimensional damped harmonics is proposed. A matrix polynomial is formed from the weighed sum of multiple shift invariances contained in the data model. Necessary and sufficient conditions are derived that reveal that the damped harmonics can be uniquely determined from the roots of the matrix polynomial. The proposed algorithm reveal a seamless link between two important classes of search free subspace methods. The classical rooting based harmonic estimation methods that exploit the complete invariance structure and the single invariance ESPRIT algorithms. We show that both approaches can be expressed under this general framework by an appropriate choice of the weights.