In order to simplify a synthesis task for particularly hard functions it is sometimes inevitable to decompose the function in a preprocessing step. We propose a new algorithm for automatically decomposing a target function by extracting a linear filter within the synthesis process. The algorithm is an application of the Linear Sifting algorithm which has been proposed by Meinel, Somenzi, and Theobald [MST97]. Using this method we were able to synthesize functions with standard tools which fail otherwise