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- W2110298963 abstract "We design a sublinear Fourier sampling algorithm for a case of sparse off-grid frequency recovery. These are signals with the form $$f(t) = sum _{j=1}^k a_j mathrm{e}^{iomega _j t} + int nu (omega )mathrm{e}^{iomega t}dmu (omega )$$ ; i.e., exponential polynomials with a noise term. The frequencies $${omega _j}$$ satisfy $$omega _jin [eta ,2pi -eta ]$$ and $$min _{ine j} |omega _i-omega _j|ge eta $$ for some $$eta > 0$$ . We design a sublinear time randomized algorithm which, for any $$epsilon in (0,eta /k]$$ , which takes $$O(klog klog (1/epsilon )(log k+log (Vert aVert _1/Vert nu Vert _1))$$ samples of $$f(t)$$ and runs in time proportional to number of samples, recovering $$omega _j'approx omega _j$$ and $$a_j'approx a_j$$ such that, with probability $$varOmega (1)$$ , the approximation error satisfies $$|omega _j'-omega _j|le epsilon $$ and $$|a_j-a_j'|le Vert nu Vert _1/k$$ for all $$j$$ with $$|a_j|ge Vert nu Vert _1/k$$ . We apply our model and algorithm to bearing estimation or source localization and discuss their implications for receiver array processing." @default.
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- W2110298963 date "2014-07-22" @default.
- W2110298963 modified "2023-10-02" @default.
- W2110298963 title "What’s the Frequency, Kenneth?: Sublinear Fourier Sampling Off the Grid" @default.
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- W2110298963 doi "https://doi.org/10.1007/s00453-014-9918-0" @default.
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