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In the analysis of High-Energy Physics data, it is frequently desired toseparate resonant signals from a smooth, non-resonant background. This paperintroduces a new technique - functional decomposition (FD) - to accomplish thistask. It is universal and readily able to describe often-problematic effectssuch as sculpting and trigger turn-ons.  Functional decomposition models a dataset as a truncated series expansion ina complete set of orthonormal basis functions, using a process analogous toFourier analysis. A new family of orthonormal functions is presented, which hasbeen expressly designed to accomplish this in a succinct way. A consistentsignal extraction methodology based on linear signal estimators is alsodetailed, as is an automated method for selecting the method's (few)hyperparameters and preventing over-fitting.  The full collection of algorithms described in this paper have beenimplemented in an easy-to-use software package, which will also be brieflydescribed.

Functional Decomposition: A new method for search and limit setting