A course of H∞0Econtrol theory
A course of H∞0Econtrol theory
Statistical Digital Signal Processing and Modeling
Statistical Digital Signal Processing and Modeling
On the Boundedness and Continuity of the Spectral Factorization Mapping
SIAM Journal on Control and Optimization
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
Extrapolation, Interpolation, and Smoothing of Stationary Time Series
A new approach to spectral estimation: a tunable high-resolutionspectral estimator
IEEE Transactions on Signal Processing
The design of approximate Hilbert transform pairs of wavelet bases
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
On the behavior of causal projections with applications
Signal Processing
Rate of convergence in approximating the spectral factor of regular stochastic sequences
IEEE Transactions on Information Theory
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Spectral factorization plays an important role in many applications such as Wiener filter design, prediction, and estimation. It is known that spectral factorization is a non-continuous mapping on the space of all non-negative continuous functions, satisfying the Paley-Wiener condition. Additionally, it will be shown in this paper that every continuous spectrum is a discontinuity point of the spectral factorization. As a consequence, small perturbations in the given data can lead to large errors in the calculated spectral factors. Practical algorithms for the calculation of the spectral factor can only use a finite number of Fourier coefficients of the given spectrum. Consequently, the error in this finite number of coefficients can yield only a finite error in the calculated spectral factor. The paper provides sharp lower and upper bounds for this error. These bounds show that this error grows proportional with the logarithm of the number N of Fourier coefficients which are taken into account.