Patrik Wahlberg

Time-frequency analysis of Gaussian stochastic processes using
the Wigner-Ville
distribution. 

Abstract:  We give an overview of time-frequency analysis using the
Wigner-Ville distribution. This is a bilinear transformation which
maps a function of one variable (time) to a function of two variables
which can be interpreted as a simultaneous distribution over time and
frequency of the function's energy. Using stochastic integration it is
possible to define the Wigner-Ville distribution of a continuous-time
Gaussian stochastic process. We describe a condition on the process
covariance function, namely it should be a member of a function space
called Feichtinger's algebra, which is sufficient to ensure the
Wigner-Ville distribution of the process has finite variance. We
exemplify an application of this theory to estimation of the so called
Wigner-Ville spectrum which is a generalization of the spectral
measure of a stationary process.