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Frequency Estimation of Irregularly Sampled Data Using a Sparsity Constrained Weighted Least-Squares Approach

Keywords: basis pursuit , sparse representation , overcomplete dictionaries , irregular sampling , spectrum estimation

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Abstract:

In this paper, a new method for frequency estimation of irregularly sampled data is proposed. In comparison with the previous sparsity-based methods where the sparsity constraint is applied to a least-squares fitting problem, the proposed method is based on a sparsity constrained weighted least-squares problem. The resulting problem is solved in an iterative manner, allowing the usage of the solution obtained at each iteration to determine the weights of the least-squares fitting term at the next iteration. Such an appropriate weighting of the least-squares fitting term enhances the performance of the proposed method. Simulation results verify that the proposed method can detect the spectral peaks using a very short data record. Compared to the previous one, the proposed method is less probable to miss the actual spectral peaks and exhibit spurious peaks.

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