Time-frequency analysis of linear signal spaces

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