Noise is suppressed in an input signal that carries a combination of noise and speech. The input signal is divided into signal blocks, which are processed to provide an estimate of a short-time perceptual band spectrum of the input signal. A determination is made at various points in time as to whether the input signal is carrying noise only or a combination of noise and speech. When the input signal is carrying noise only, the corresponding estimated short-time perceptual band spectrum of the input signal is used to update an estimate of an long term perceptual band spectrum of the noise. A noise suppression frequency response is then determined based on the estimate of the long term perceptual band spectrum of the noise and the short-time perceptual band spectrum of the input signal, and used to shape a current block of the input signal in accordance with the noise suppression frequency response.