Abstract: An adaptive filter for the approximation of a read-in set function F in a function space, containing a set of elementary filters g.sub.b, n being an integer .gtoreq.1. The elementary filters cover a sub-space in the function space, the parameters of the elementary filter are changable and the filter performs the following operation: calculating the normal projections of the set function F on each elementary filter and multiplying the normal projection quantities A.sub.a thus obtained by the contra-variant metric tensor G.sup.ab formed from the set of the elementary filters in order thereby to obtain the projection of the set function F on the sub-space covered, whose difference D from the set function F is determined as a function of the elementary filter and the metric tensor in accordance with the formula (I) in order thereby to minimise the difference D by changing the elementary filter parameters by means of conventional deterministic (e.g. "gradient fall method") or stochastic (e.g.