We study a problem of locating and estimating singularities of a signal measured with noise on a discrete set of points (fixed-design model). The signal consists of a smooth part with bounded first derivative and of finite number of singularities of the type (x − ti) p ± di, 0 ≤ p ≤ 1. The case p = 0 corresponds to a 2 piecewise continuous function. The algorithm is based on convolving the data with a kernel having compact support. Optimal bandwidth of the kernel is calculated, the consistency of the algorithm is proved. The results of testing of the proposed algorithm on model examples are presented
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