A course of H∞0Econtrol theory
A course of H∞0Econtrol theory
Probability (2nd ed.)
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
MIMO decision feedback equalization from an H∞ perspective
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
On the Calculation of the Hilbert Transform From Interpolated Data
IEEE Transactions on Information Theory
MMSE decision-feedback equalizers: finite-length results
IEEE Transactions on Information Theory
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Common methods for the calculation of the spectral factorization rely on an approximation of the given spectral density by a polynomial and a subsequent factorization of this polynomial. It is known that the regularity of the stochastic sequence determines the achievable approximation rate of its spectrum. However, since the approximative polynomial should be factorized, it has to be positive. It is shown that this restriction on the approximation polynomial implies a limitation on the approximation rate for linear methods whereas for nonlinear methods the optimal approximation rate can still be achieved. This has also consequences for the rate of convergence of the spectral factor, which is investigated in the second part. There, a lower and an upper bound for the error in the spectral factor is derived, which shows the dependency on the approximation degree and on the regularity of the stochastic sequence. Finally, if the spectral density is given only on a finite set of sampling points, no linear approximation method exists such that the error in the spectral factor can be controlled by the approximation degree.