  In the analysis of High-Energy Physics data, it is frequently desired to
separate resonant signals from a smooth, non-resonant background. This paper
introduces a new technique - functional decomposition (FD) - to accomplish this
task. It is universal and readily able to describe often-problematic effects
such as sculpting and trigger turn-ons.
  Functional decomposition models a dataset as a truncated series expansion in
a complete set of orthonormal basis functions, using a process analogous to
Fourier analysis. A new family of orthonormal functions is presented, which has
been expressly designed to accomplish this in a succinct way. A consistent
signal extraction methodology based on linear signal estimators is also
detailed, 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 been
implemented in an easy-to-use software package, which will also be briefly
described.
