High-performance variable band-pass/band-stop state-space digital filters using Gramian-preserving frequency transformation

Shunsuke Koshita, Keita Miyoshi, Masahide Abe, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This paper presents a simple state-space-based method for design and realization of variable band-pass/band-stop IIR digital filters. Our proposed variable filters not only allow us to tune the frequency characteristics, but also ensure high-performance with respect to finite wordlength effects such as L2-norm dynamic range scaling, limit cycles, roundoff noise, and coefficient sensitivity. We achieve this property using the Gramian-preserving frequency transformation, which is implemented by replacing each delay element in a given prototype filter with a second-order all-pass function that has the four-multiplier-lattice structure. It is shown that our proposed variable filters are described in a rather simple form without the need of the inverse matrix that appeared in the conventional Gramian-preserving frequency transformation. Moreover, we show the high-performance of our proposed method in comparison with other possible types of frequency transformations that are implemented by the typical one-multiplier/two-multiplier-lattice forms and the direct form.

Original languageEnglish
Pages (from-to)175-184
Number of pages10
JournalDigital Signal Processing: A Review Journal
Issue number1
Publication statusPublished - 2014


  • Finite wordlength effect
  • Four-multiplier- lattice structure
  • Gramian-preserving frequency transformation
  • State-space representation
  • Variable digital filter

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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