Time frequency weighting and displacement effects in linear, time-varying systems

When a signal passes through a linear, time-varying (LTV) system various signal components are weighted (attenuated or amplified) and displaced in the time-frequency (TF) plane. A gross description of TF displacement effects is provided by centroids and spreads whose definition is based on the Wigner distribution. The classes of normal, time-invariant, frequency-invariant, and unitary systems are considered, and the class of systems minimizing FF displacement (for fixed TF weighting) is derived. The polar decomposition of LTV systems is shown to provide a separation of weighting and displacement effects