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arXiv · 2410.12349

When atomic norm meets the G-filter: A general framework for line spectral estimation

Bin Zhu·Jiale Tang
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Abstract

This paper proposes a novel approach for line spectral estimation which combines Georgiou's filter bank (G-filter) with atomic norm minimization (ANM). A key ingredient is a Carath\'{e}odory--Fej\'{e}r-type decomposition for the covariance matrix of the filter output. The resulting optimization problem can be characterized via semidefinite programming and contains the standard ANM for line spectral estimation as a special case. Simulations show that our approach outperforms the standard ANM in terms of recovering the number of spectral lines when the signal-to-noise ratio is no lower than 0 dB and the G-filter is suitably designed.

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Bin Zhu, Jiale Tang. 2024-10-16. When atomic norm meets the G-filter: A general framework for line spectral estimation. https://arxiv.org/abs/2410.12349

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