A noise cancellation system, comprising: an input for a digital signal, the digital signal having a first sample rate; a digital filter, connected to the input to receive the digital signal; a decimator, connected to the input to receive the digital signal and to generate a decimated signal at a second sample rate lower than the first sample rate; and a processor. The processor comprises: an emulation of the digital filter, connected to receive the decimated signal and to generate an emulated filter output; and a control circuit, for generating a control signal on the basis of the emulated filter output. The control signal is applied to the digital filter to control a filter characteristic thereof.