IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Optimal kernels for nonstationary spectral estimation
IEEE Transactions on Signal Processing
Spectral smoothing and recursion based on the nonstationarity ofthe autocorrelation function
IEEE Transactions on Signal Processing
Discrete-time, discrete-frequency, time-frequency analysis
IEEE Transactions on Signal Processing
An overview of aliasing errors in discrete-time formulations oftime-frequency representations
IEEE Transactions on Signal Processing
Shift covariant time-frequency distributions of discrete signals
IEEE Transactions on Signal Processing
Alias-free generalized discrete-time time-frequency distributions
IEEE Transactions on Signal Processing
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In stochastic time-frequency analysis, the covariance function is often estimated from only one observed realization with the use of a kernel function. For processes in continuous time, this can equivalently be done in the ambiguity domain, with the advantage that the mean square error optimal ambiguity kernel can be computed. For processes in discrete time, several ambiguity domain definitions have been proposed. It has previously been reported that in the Jeong-Williams ambiguity domain, in contrast to the Nutall and the Claasen-Mecklenbrauker ambiguity domain, any smoothing covariance function estimator can be represented as an ambiguity kernel function. In this paper, we show that the Jeong-Williams ambiguity domain cannot be used to compute the mean square error (MSE) optimal covariance function estimate for processes in discrete time. We also prove that the MSE optimal estimator can be computed without the use of the ambiguity domain, as the solution to a system of linear equations. Some properties of the optimal estimator are derived.