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Generalizing Caratheodory's uniqueness of harmonic parameterization to N dimensions

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1 Author(s)
Sidiropoulos, N.D. ; Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN, USA

Consider a sum of F exponentials in N dimensions, and let In be the number of equispaced samples taken along the nth dimension. It is shown that if the frequencies or decays along every dimension are distinct and Σn=1N In ⩾2F+(N-1), then the parameterization in terms of frequencies, decays, amplitudes, and phases is unique. The result can be viewed as generalizing a classic result of Caratheodory to N dimensions. The proof relies on a recent result regarding the uniqueness of low-rank decomposition of N-way arrays

Published in:

Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 4 )

Date of Publication:

May 2001

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