Finite-time-averaged power spectra and signal energy distribution in time and frequency (Corresp.)

Abstract

In response to a recent paper, this correspondence points out the difficulty of applying the concept of the energy distribution in time and frequency of deterministic signals to random signals and finite-time-averaged power spectra. For deterministic signals, an appropriately defined finite-time spectrum will indicate the frequency band within which the signal energy is concentrated at a particular time. However, it does not appear meaningful to apply such concepts to finite-time averages of random processes since taking sample averages would typically destroy any time-frequency distribution of the energy perhaps found in an individual sample of the process.