Extracting Phases from Aperiodic Signals
  We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive phase velocities is proposed as an old solution to this new problem. 
Alexander Kraskov, Thomas Kreuz, Ralph G. Andrzejak, Harald   Stoegbauer, Walter Nadler and Peter Grassberger