The invention relates to a linear prediction audio signal processing apparatus, such as a vocoder, including a nonlinear filter to attenuate the residual signal used to excite a linear prediction synthesis filter. The nonlinear filter is capable of reducing the noise component in the signal while keeping only the periodic component of the speech signal. This feature enhances speech quality. The invention also extends to a novel method for processing a residual signal used to excite a linear prediction synthesis filter in order to attenuate wide band additive noise in the speech signal as constructed by the synthesis filter.