In a system for estimating the power spectral density of acoustical background noise when the level of a smoothed power spectral density signal increases, an increment value is increased, starting from a minimum increment value, by a predetermined amount until a maximum increment value is reached if at the same time the value of the power spectral density currently determined in a new calculation cycle is larger than the estimate value of the power spectral density of the background noise determined in the previous calculation cycle. For cases in which the level of the smoothed power spectral density decreases, the amplitude of the decrement value is increased, starting from a minimum decrement value, by a predetermined amount until a maximum decrement value is reached if at the same time the value of the power spectral density currently determined in a new calculation cycle is smaller than the estimate value of the power spectral density of the background noise determined in the previous calculation cycle.