| Hi-index | 754.84 |
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