REGULARIZATION OF KERNELS FOR ESTIMATION OF THE WIGNER
SPECTRUM OF GAUSSIAN STOCHASTIC PROCESSES
Abstract: We study estimation of the Wigner 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.
2000 AMS Mathematics Subject Classification: Primary: 60G15, 42B35, 60G35,
62M15, 94A12.
Keywords and phrases: Time-frequency analysis, Gaussian stochastic processes, Wigner
distribution, Wigner spectrum, minimum mean square error estimation, Cohen’s class, the
Feichtinger algebra.