We consider a signal reconstruction problem for signals F of the form F(x) = Σdj=1 ajδ(x-xj) from their Fourier transform F(F)(s) = ∫∞-∞ F(x)e-isxdx. We assume F(F)(s) to be known for each s ε [-Ν,Ν] with an absolute error not exceeding ε > 0. We give an absolute lower bound (which is valid with any reconstruction method) for the 'worst case' reconstruction error of F from F(F) for situations where the xj nodes are known to form an I elements cluster contained in an interval of length h << 1. Using 'decimation' algorithm of ,  we provide an upper bound for the reconstruction error, essentially of the same form as the lower one. Roughly, our main result states that for h of order 1/N 1/2l-1 the worst case reconstruction error of the cluster nodes is of the same order 1/N 1/2l-1, and hence the inside configuration of the cluster nodes (in the worst case scenario) cannot be reconstructed at all. On the other hand, decimation algorithm reconstructs F with the accuracy of order 1/N 1/2l.