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.
- Multidimensional harmonic retrieval
- Multiway analysis
- PARAllel FACtor (PARAFAC) analysis
- Spectral analysis