Estimating the Frequency of a Clustered Signal

  title={Estimating the Frequency of a Clustered Signal},
  author={Xue Chen and Eric Price},
We consider the problem of locating a signal whose frequencies are "off grid" and clustered in a narrow band. Given noisy sample access to a function $g(t)$ with Fourier spectrum in a narrow range $[f_0 - \Delta, f_0 + \Delta]$, how accurately is it possible to identify $f_0$? We present generic conditions on $g$ that allow for efficient, accurate estimates of the frequency. We then show bounds on these conditions for $k$-Fourier-sparse signals that imply recovery of $f_0$ to within $\Delta… 
4 Citations

Sample Efficient Toeplitz Covariance Estimation

A new covariance estimation strategy is developed that further improves on all existing methods in the low-rank case and achieves sample complexity depending polynomially on $k$ and only logarithmically on $d$.

Fourier Sparse Leverage Scores and Approximate Kernel Learning

New explicit upper bounds on the leverage scores of Fourier sparse functions under both the Gaussian and Laplace measures are proved, which generalize existing work that only applies to uniformly distributed data.

(Nearly) Sample-Optimal Sparse Fourier Transform in Any Dimension; RIPless and Filterless

This algorithm uses O(k log k log n) samples, is dimension-free, operates for any universe size, and achieves the strongest ℓ_∞/ℓ-2 guarantee, while running in a time comparable to the Fast Fourier Transform.

The Statistical Cost of Robust Kernel Hyperparameter Tuning

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An algorithm for finding a Fourier representation of B for a given discrete signal signal A, such that A is within the factor (1 +ε) of best possible $\|\signal-\repn_\opt\|_2^2$.

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It is shown how to estimate the signal with a constant factor growth of the noise and sample complexity polynomial in k and logarithmic in the bandwidth and signal-to-noise ratio for arbitrary k-Fourier-sparse signals under l2 bounded noise.

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This work extends tools based on statistical leverage score sampling and column-based matrix reconstruction to the approximation of continuous linear operators that arise in the signal reconstruction problem, based on a novel connection between randomized linear algebra and the problem of reconstructing signals with constrained Fourier structure.

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  • Eric PriceZhao Song
  • Computer Science
    2015 IEEE 56th Annual Symposium on Foundations of Computer Science
  • 2015
An algorithm for robustly computing sparse Fourier transforms in the continuous setting and new results for how precisely the individual frequencies of x* can be recovered are given.

Simple and practical algorithm for sparse Fourier transform

This work considers the sparse Fourier transform problem, and proposes a new algorithm, which leverages techniques from digital signal processing, notably Gaussian and Dolph-Chebyshev filters, and is faster than FFT, both in theory and practice.

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A significantly improved algorithm for the problem of finding a Fourier representation R of m terms for a given discrete signal A of length N and a quadratic-in-m algorithm that works for any values of Ni's is given.

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  • P. IndykM. Kapralov
  • Computer Science
    2014 IEEE 55th Annual Symposium on Foundations of Computer Science
  • 2014
An algorithm for sparse recovery from Fourier measurements using O(k log N) samples, matching the lower bound of Do Ba-Indyk-Price-Woodruff'10 for non-adaptive algorithms up to constant factors for any k ≤ N<sup>1-δ</sup>.

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  • Computer Science, Mathematics
    SIAM J. Comput.
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