The present disclosure relates to adaptive filtering optimization methods based on a hyperbolic sine cost function. While the adaptive filtering optimization methods belong to the variable step-size class, however, the present disclosure describes a new approach requiring tuning of only one parameter. The present disclosure is further related to a family of higher order hyperbolic sine cost functions.

A signal processor includes: a first adaptive filter that takes a first signal as input and generates a first pseudo signal; a first subtractor that subtracts the first pseudo signal from a second signal to supply a first differential signal as output; a second adaptive filter that takes the first signal as input to generate a second pseudo signal; a second subtractor that subtracts the second pseudo signal from the second signal to supply a second differential signal as output; a first step size control circuit that generates a first step size used in updating the first adaptive filter in accordance with the relation between the second pseudo signal and the second differential signal; and a second step size control circuit that generates a second step size used in updating the second adaptive filter in accordance with the relation between the first signal and the second signal.