A method is provided for recurrently estimating a spectrum of noise at each signal observation interval from a sound signal which contains the noise and which is observed at each signal observation interval. In the method, there are acquired an envelope of a previous spectrum of the noise which has been previously estimated from the sound signal observed at a previous signal observation interval, and an envelope of a current spectrum of the sound signal which is observed at a current signal observation interval subsequent to the previous signal observation interval. Then, a value of correlation is computed between the envelop of the previous spectrum of the noise and the envelope of the current spectrum of the sound signal. A current spectrum of the noise contained in the sound signal observed at the current signal observation interval is estimated in accordance with the computed value of the correlation and based on the previous spectrum of the noise and the current spectrum of the sound signal.