A background noise estimate based upon a modified Doblinger noise estimate is used for modulating the output of a pseudo-random phase spectrum generator to produce the comfort noise. The circuit for estimating noise includes a smoothing filter having a slower time constant for updating the noise estimate during noise than during speech. Comfort noise is smoothly inserted by basing the amount of comfort noise on the amount of noise suppression. A discrete inverse Fourier transform converts the comfort noise back to the time domain and overlapping windows eliminate artifacts that may have been produced during processing.