| Session: | 1.1.7 - Communication Systems I |
| Session Time: | Monday, July 10, 09:40 - 11:00 |
| Paper Time: | Monday, July 10, 09:40 - 10:00 |
| Title: |
There exits no always convergent algorithm for the calculation of spectral factorization, Wiener filter, and Hilbert transform |
| Authors: |
Holger Boche; Technical University of Berlin | | |
| | Volker Pohl; Technical University of Berlin | | |
| Abstract: |
Spectral factorization, Wiener filtering, and many other important operations in information theory and signal processing can be lead back to a Hilbert transform and a Poisson integral. Whereas the Poisson integral causes generally no problems, the Hilbert transform has a much more complicated behavior. This paper investigates the possibility to calculate the Hilbert transform $\widetilde{f}$ of a given continuous function $f$ based on a finite set of sampling points of $f$. It shows that even if $\widetilde{f}$ is continuous, no linear approximation operator exists which approximates $\widetilde{f}$ arbitrary well from a finite number of sampling points of $f$, in general. Moreover, the paper characterizes the set of all functions for which such linear approximation operators exist and discusses some consequences for practical applications. |
