System representations for the zakai class with applications

Holger Boche, Ullrich J. Monich

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The convergence behavior of a convolution representation of stable linear time-invariant (LTI) systems operating on the Zakai class of bandlimited signals is analyzed. It is shown that there are signals in the Zakai class for which the convolution integral diverges if the system is the Hilbert transform or the ideal low-pass filter with bandwidth less than or equal to the signal bandwidth. Moreover, using a previously obtained result of Habib, it is proved that the class of stable LTI systems that map the Zakai class into itself does not include the Hilbert transform and the ideal low-pass filter with bandwidth less than or equal to the signal bandwidth. Finally, it is shown that the concept of the analytical signal, which is used in communications, is problematic for the signal space Zπ, because the operator for its computation is unbounded and discontinuous.

Original languageEnglish
Article number5508604
Pages (from-to)4129-4134
Number of pages6
JournalIEEE Transactions on Information Theory
Volume56
Issue number8
DOIs
StatePublished - Aug 2010
Externally publishedYes

Keywords

  • Analytical signal
  • Hilbert transform
  • Zakai class
  • bandlimited signal
  • convolution integral
  • ideal low-pass filter
  • system representation

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