Generalizing Carathèodory's Uniqueness of Harmonic Parameterization to N dimensions

N. D. Sidiropoulos

Research output: Contribution to journalLetterpeer-review

42 Scopus citations


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 dimensions are distinct and ∑n=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 Carathéodory to N dimensions. The proof relies on a recent result regarding the uniqueness of low-rank decomposition of N-way arrays.

Original languageEnglish (US)
Pages (from-to)1687-1690
Number of pages4
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - May 2001


  • Multidimensional harmonic retrieval
  • Multiway analysis
  • PARAllel FACtor (PARAFAC) analysis
  • Spectral analysis
  • Uniqueness


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