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On the instantaneous frequency of Gaussian stochastic processes

Wahlberg P., Schreier P. J.

Probability and Mathematical Statistics

2012

Vol. 32, Fasc. 1

69--92

We study the instantaneous frequency (IF) of continuoustime, complex-valued, zero-mean, proper, mean-square differentiable, nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum.

Regularization of kernels for estimation of the wigner spectrum of Gaussian stochastic processes

Wahlberg P.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 2

369--381

We study estimation of theWigner time-frequency spectrum of Gaussian stochastic processes. Assuming the covariance belongs to the Feichtinger algebra, we construct an estimation kernel that gives a mean square error arbitrarily close to the infimum over kernels in the Feichtinger algebra.