A signal processor for processing a digital input signal including samples sampled at a sampling frequency, the signal processor comprising a plurality of filters arranged to divide the digital input signal into a first signal in a first frequency band below a first cut-off frequency, and a second signal in a second frequency band above a second cut-off frequency; first frequency shifting circuitry arranged to shift the second signal to a frequency band below the first cut-off frequency; decimation circuitry arranged to decimate the first signal and the shifted second signal; and processing circuitry arranged to process the decimated first and second signals.