In a method for fast decoding of the output signals of sigma delta modulators, the decoded output signal of a modulator is acquired using a sequence of iteration steps. In each step, two operations P.sub.1 or, respectively, P.sub.2 are thereby successively implemented, whereby the signals s are presented by components s(n), s(n-1), s(n-2), . . . , s(n-k) that are temporal samples of these signals. The operation P.sub.1 is a projection in the space of all input signals of the modulator onto the set of all of those input signals that the modulator images onto the output signal to be decoded. The operation P.sub.2 is a projection onto the sub-space of all band-limited input signals of the modulator. A presentation of the signals is selected for both operations wherein the operation P.sub.1 can be implemented component-by-component. This method is substantially faster (10.sup.4 -10.sup.5) than all known methods for decoding the output signals of sigma delta modulators with comparable precision and is only 2-10 times slower than substantially more imprecise, linear decoding methods. It can be employed in conjunction with all standard sigma delta architectures.