A speech enhancement system for the reduction of background noise comprises a time-to-frequency transformation unit (2) to transform frames of time-domain samples of audio signals to the frequency domain, background noise reduction means (3) to perform noise reduction in the frequency domain, and a frequency-to-time transformation unit (4) to transform the noise reduced signals back to the time-domain. In the background noise reduction means (3) for each frequency component a predicted background magnitude is calculated in response to the measured input magnitude from the time-to-frequency transformation unit (2) and to the previously calculated background magnitude, whereupon for each of said frequency components the signal-to-noise ratio is calculated in response to the predicted background magnitude and to said measured input magnitude and the filter magnitude for said measured input magnitude in response to the signal-to-noise ratio. The speech enhancement device may be applied in speech coding systems, particularly P2CM coding systems.