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- W2278969531 abstract "We consider the problem of algebraic of linear combinations of shifts of several known signals $f_1,ldots,f_k$ from the Fourier samples. Following cite{Bat.Sar.Yom2}, for each $j=1,ldots,k$ we choose sampling set $S_j$ to be a subset of the common set of zeroes of the Fourier transforms ${cal F}(f_ell), ell ne j$, on which ${cal F}(f_j)ne 0$. It was shown in cite{Bat.Sar.Yom2} that in this way the reconstruction system is decoupled into $k$ separate systems, each including only one of the signals $f_j$. The resulting systems are of a generalized Prony form. However, the sampling sets as above may be non-uniform/not dense enough to allow for a unique reconstruction of the shifts and amplitudes. In the present paper we study uniqueness and robustness of non-uniform Fourier sampling of signals as above, investigating sampling of exponential polynomials with purely imaginary exponents. As the main tool we apply a well-known result in Harmonic Analysis: the Turan-Nazarov inequality (cite{Naz}), and its generalization to discrete sets, obtained in cite{Fri.Yom}. We illustrate our general approach with examples, and provide some simulation results." @default.
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- W2278969531 date "2013-11-14" @default.
- W2278969531 modified "2023-09-27" @default.
- W2278969531 title "Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals" @default.
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