The Wigner distribution of a linear signal space

摘要

A time-frequency representation of linear signal spaces, called its Wigner distribution (WD), is introduced. Similar to the WD of a signal, the WD of a linear signal space describes the space's energy distribution over the time-frequency plane. It is shown that the WD of a signal space can be defined both in a deterministic and in a stochastic framework, and it can be expressed in a simple way in terms of the space's projection operator and the bases. It is shown to satisfy many interesting properties which are often analogous to corresponding properties of the WD of a signal. The results obtained for some specific signal spaces are found to be intuitively satisfactory. The cross-WD of two signal spaces, a discrete-time WD version, and the extension of the WD definition to arbitrary quadratic signal representation are also discussed.