Title :
Generalizing Caratheodory´s uniqueness of harmonic parameterization to N dimensions
Author :
Sidiropoulos, Nicholas D.
Author_Institution :
Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN, USA
fDate :
5/1/2001 12:00:00 AM
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 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
Keywords :
harmonic analysis; multidimensional signal processing; signal sampling; spectral analysis; F exponentials; N dimensions; N-way arrays; PARAFAC; amplitudes; decays; equispaced samples; frequencies; generalizing Caratheodory´s uniqueness; harmonic parameterization; low-rank decomposition; multidimensional harmonic retrieval; multiway analysis; phases; spectral analysis; Closed-form solution; Delay estimation; Frequency estimation; Harmonic analysis; Multidimensional signal processing; Random processes; Signal processing; Signal processing algorithms; Spectral analysis; Stochastic processes;
Journal_Title :
Information Theory, IEEE Transactions on
