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arXiv · 1305.2832

Decoupling of Fourier Reconstruction System for Shifts of Several Signals

Dmitry Batenkov·Niv Sarig·Yosef Yomdin
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Abstract

We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of zeroes of the Fourier transforms ${\cal F}(f_\l), \ \l \ne r$, on which ${\cal F}(f_r)\ne 0$. We show that in this way the reconstruction system is reduced to $k$ separate systems, each including only one of the signals $f_r$. Each of the resulting systems is of a ``generalized Prony'' form. We discuss the problem of unique solvability of such systems, and provide some examples.

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Dmitry Batenkov, Niv Sarig, Yosef Yomdin. 2013-05-13. Decoupling of Fourier Reconstruction System for Shifts of Several Signals. https://arxiv.org/abs/1305.2832

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