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We consider Fourier reconstruction problem for signals F, which are linearcombinations of shifted delta-functions. We assume the Fourier transform of Fto be known on the frequency interval [-N,N], with an absolute error notexceeding e > 0. We give an absolute lower bound (which is valid with anyreconstruction method) for the "worst case" reconstruction error of F insituations where the nodes (i.e. the positions of the shifted delta-functionsin F) are known to form an l elements cluster of a size h << 1. Using"decimation" reconstruction algorithm we provide an upper bound for thereconstruction error, essentially of the same form as the lower one. Roughly,our main result states that for N*h of order of (2l-1)-st root of e the worstcase reconstruction error of the cluster nodes is of the same order as h, andhence the inside configuration of the cluster nodes (in the worst casescenario) cannot be reconstructed at all. On the other hand, decimationalgorithm reconstructs F with the accuracy of order of 2l-st root of e.

Accuracy of spike-train Fourier reconstruction for colliding nodes