A new approach to moving-average filtering is proposed, based on a mathematical description of an input mixture as a finite sum of sinusoidal segments. The proposed filter possesses some advantages: it is efficient when processing very short-duration mixtures and, additionally, the restriction on the closeness of the frequencies of the mixture components is determined only by the resolution of a computer. Among filter's other properties a high precision of useful signal recovery and a relative simplicity of construction should be mentioned. Algorithms and the results of computer simulations of the filter's performance in different noise environment are presented.