Gramian-preserving frequency transformation for linear discrete-time state-space systems

Shunsuke Koshita, Satoru Tanaka, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass, system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems. Copyright

Original languageEnglish
Pages (from-to)3014-3021
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number10
Publication statusPublished - 2008 Oct
Externally publishedYes


  • Abservability Gramian
  • Allpass function
  • Controllability Gramian
  • Discrete-time state-space system
  • Frequency transformation
  • Normalized lattice structure

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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