A noise-suppression circuit (10) divides the signal from a microphone (12) into a plurality of frequency sub-bands by means of a noise-band divider (18) and a subtraction circuit (36). By means of gain circuits (32) and (34), it applies separate gains to the separate bands and then recombines them in a signal combiner (38) to generate an output signal in which the noise has been suppressed. Separate gains are applied only to the lower subbands in the voice spectrum. Accordingly, the noise-band divider (18) is required to compute spectral components for only those bands. By employing a sliding-discrete-Fourier-transform method, the noise-band divider (18) computes the spectral components on a sample-by-sample basis, and circuitry (50, 52) for determining the individual gains can therefore update them on a sample-by-sample basis, too.