Invariance of second-order modes under frequency transformation in 2-D separable denominator digital filters

Shunsuke Koshita, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

This paper discusses the invariance of the second-order modes of 2-D separable denominator digital filters under frequency transformation. This paper first derives a state-space description for 2-D digital filters obtained by 2-D frequency transformation and then represents the controllability Gramians and the observability Gramians of the transformed 2-D digital filters. This description proves that the second-order modes of 2-D separable denominator digital filters are not invariant under all frequency transformations, but invariant under specific frequency transformations of which transfer functions are strictly proper. These frequency transformations include lowpass-bandpass and lowpass-bandstop frequency transformations keeping the same bandwidth as that of the prototype lowpass filter. It is also shown that the horizontal second-order modes are invariant when only horizontal transformation is applied, and the vertical second-order modes are invariant when only vertical transformation is applied. This paper further remarks significance brought by the invariance of the second-order modes under frequency transformation.

Original languageEnglish
Pages (from-to)305-333
Number of pages29
JournalMultidimensional Systems and Signal Processing
Volume16
Issue number3
DOIs
Publication statusPublished - 2005 Jul

Keywords

  • 2-D digital filter
  • Frequency transformation
  • Second-order mode
  • Separable denominator
  • State equation

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Information Systems
  • Hardware and Architecture
  • Computer Science Applications
  • Artificial Intelligence
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Invariance of second-order modes under frequency transformation in 2-D separable denominator digital filters'. Together they form a unique fingerprint.

Cite this