A method of noise suppression to suppress noise in a signal containing background noise (314) in a communications path between a cellular communications network and a mobile terminal. The method comprises the steps of: estimating and up-dating a spectrum of the background noise (332, 334); using the background noise spectrum to suppress noise in the signal; generating an indication to indicate the operation of at least one of a discontinuous transmission unit (DTX) and a bad frame handling unit (BFI); and freezing estimating and up-dating of the spectrum of the background noise when the indication is present.