Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Rate of convergence in approximating the spectral factor of regular stochastic sequences
 IEEE transactions on information theory 55 (2009), No.12, pp.56745681 ISSN: 00189448 

 English 
 Journal Article 
 Fraunhofer HHI () 
Abstract
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.