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

Volume

47

Issue

4

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

1687

Lastpage

1690

Abstract

Consider a sum of F exponentials in N dimensions, and let I_n 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 Σ_n=1^N I_n⩾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;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.923759

Filename

923759