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Regularization of kernels for estimation of the Wigner spectrum of Gaussian stochastic processes. (English) Zbl 1230.62126

Summary: We study estimation of the Wigner time-frequency spectrum of Gaussian stochastic processes. Assuming the covariance belongs to the Feichtinger algebra [H.G. Feictinger, Monatsh. Math. 92, 269–289 (1981; Zbl 0461.43003)], we construct an estimation kernel that gives a mean square error arbitrarily close to the infimum over the kernels in the Feichtinger algebra.

MSC:

62M15 Inference from stochastic processes and spectral analysis
43A20 \(L^1\)-algebras on groups, semigroups, etc.

Citations:

Zbl 0461.43003
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