In this paper we apply a recursive deconvolution method to active noise cancellation (ANC) in a linear system: the observation of the output of a linear system of relative degree one, read at discrete time instants, is fed to a deconvolution algorithm which identifies the disturbance (with the delay of one step). This information is used in order to reduce the effect of the disturbance itself. Deconvolution being an ill posed problem, a regularization parameter is to be introduced. The choice of the value of the parameter is a delicate issue. We show that, when studying ANC, the discrepancy principle (applied recursively) is a feasible method for the choice of the parameter.