For fixed A, N, L > 0, consider the set M of all L2 functions (signals) on the real line whose spectrum (i.e. support of the Fourier transform) is contained in the interval [-A, A] and simultanuosly in a sum of N intervals, each of length at most L (which can be positioned anywhere inside the interval [-A, A]). Blind multiband sampling deals with the problem of existence of a (stable) sampling set for M, i.e. a discrete subset of the real line, such that the signal from M is uniquely determined by its values on this set. During the talk I would present effective (yet, in general, not providing perfect reconstruction) algorithms for blind multiband sampling proposed by Y. Eldar and C. Mishali, which are based on the idea of compressed sensing.