# Fourier-Sparse Interpolation without a Frequency Gap

@article{Chen2016FourierSparseIW,
title={Fourier-Sparse Interpolation without a Frequency Gap},
author={Xue Chen and Daniel M. Kane and Eric Price and Zhao Song},
journal={2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)},
year={2016},
pages={741-750}
}
• Published 6 September 2016
• Computer Science
• 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
We consider the problem of estimating a Fourier-sparse signal from noisy samples, where the sampling is done over some interval [0, T] and the frequencies can be "off-grid". Previous methods for this problem required the gap between frequencies to be above 1/T, the threshold required to robustly identify individual frequencies. We show the frequency gap is not necessary to estimate the signal as a whole: for arbitrary k-Fourier-sparse signals under l2 bounded noise, we show how to estimate the…

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