Abstract
This paper derives a novel property of the secondorder modes of discrete-time systems under variable transformation. This is the generalization of the theory presented by Mullis and Roberts, who discovered the invariance of the second-order modes under allpass transformation (variable transformation of lossless bounded-real function) and the relationship of this invariance to the roundoff noise of digital filters. This paper proves that the values of the second-order modes are decreased under any variable transformation of bounded-real function. The proof is achieved with the help of the bounded-real lemma and formulation of the controllability and observability Gramians of transformed discrete-time systems.
Original language | English |
---|---|
Article number | 1464752 |
Pages (from-to) | 972-975 |
Number of pages | 4 |
Journal | Proceedings - IEEE International Symposium on Circuits and Systems |
DOIs | |
Publication status | Published - 2005 |
Externally published | Yes |
Event | IEEE International Symposium on Circuits and Systems 2005, ISCAS 2005 - Kobe, Japan Duration: 2005 May 23 → 2005 May 26 |
ASJC Scopus subject areas
- Electrical and Electronic Engineering