Abstract
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 language | English (US) |
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Pages (from-to) | 1687-1690 |
Number of pages | 4 |
Journal | IEEE Transactions on Information Theory |
Volume | 47 |
Issue number | 4 |
DOIs | |
State | Published - May 2001 |
Externally published | Yes |
Keywords
- Multidimensional harmonic retrieval
- Multiway analysis
- PARAllel FACtor (PARAFAC) analysis
- Spectral analysis
- Uniqueness