Rooting-Based Harmonic Retrieval Using Multiple Shift-Invariances: The Complete and the Incomplete Sample Cases

In the present paper, we propose a novel method for estimating one-dimensional damped and undamped harmonics. Our method utilizes the multiple shift-invariance property comprised in the signal model. We develop a new rank-reduction estimator which is formed as the weighted sum of the individual matr...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2012-04, Vol.60 (4), p.1556-1570
Main Authors: Parvazi, P., Pesavento, M., Gershman, A. B.
Format: Article
Language:English
Subjects:
Algorithms
Ambiguity
Applied sciences
Covariance matrix
Criteria
Detection, estimation, filtering, equalization, prediction
Direction of arrival estimation
Estimates
Estimation
Estimators
Exact sciences and technology
Frequency estimation
Harmonic analysis
harmonic retrieval
Harmonics
incomplete data
Information, signal and communications theory
Mathematical analysis
Mathematical model
matrix polynomial
polynomial rooting
Polynomials
rank-reduction estimator
shift-invariance property
Signal and communications theory
Signal, noise
Studies
Telecommunications and information theory
Uniqueness
Vectors
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Summary:In the present paper, we propose a novel method for estimating one-dimensional damped and undamped harmonics. Our method utilizes the multiple shift-invariance property comprised in the signal model. We develop a new rank-reduction estimator which is formed as the weighted sum of the individual matrix polynomials obtained from individual shift-invariance equations. The uniqueness conditions for the proposed rank-reduction criteria are derived under the assumption that all samples are available. Moreover, a novel technique for the incomplete data case, where some samples are missing, is presented. In this case, the rank-reduction estimator may suffer from ambiguities. To overcome this problem, we propose an extension of the rank-reduction estimator that is based on polynomial intersection and the properties of the Sylvester matrix. The latter algorithm yields unique estimates of the damped harmonics. The proposed high-resolution techniques are search-free and therefore, they enjoy moderate computational complexity.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2011.2181840