Optimal linear filtering has been used extensively for speech enhancement. In this paper, we take a first step in trying to apply linear filtering to the decomposition of a noisy speech signal into its components. The problem of decomposing speech into its voiced and unvoiced components is considered as an estimation problem. Assuming a harmonic model for the voiced speech, we propose a Wiener filtering scheme which estimates both components separately in the presence of noise. It is shown under which conditions this optimal filtering formulation outperforms two state-of-the-art speech decomposition methods, which is also revealed by objective measures, spectrograms and informal listening tests. Index Terms-Speech decomposition, time-domain filtering, Wiener filter, voiced speech, unvoiced speech.