Time-frequency analysis of linear signal spaces

Abstract

The authors introduce the Wigner distribution (WD) of a linear signal space and show how this concept can be used for the time-frequency analysis and synthesis of linear signal spaces and the optimal design of time-frequency projection filters. The WD of a linear signal space describes the space's energy distribution over the time-frequency plane and possesses many interesting properties. It can be expressed as the Weyl symbol of the space's projection operator or, alternatively, as the sum of WDs of all basis signals. As an analysis tool, the WD of a signal space characterizes the space's time-frequency localization. From the WD, parameters can be derived which allow a global quantitative characterization of localization and concentration properties, and inequalities bounding these parameters can be shown to exist. >