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

• Published in: Digital signal processing Vol. 27; pp. 175 - 184
• Main Authors: Koshita, Shunsuke, Miyoshi, Keita, Abe, Masahide, Kawamata, Masayuki
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2014
• Subjects: Delay; Digital filters; Digital signal processing; Dynamic range; Finite wordlength effect; Four-multiplier-lattice structure; Gramian-preserving frequency transformation; Inverse; Mathematical analysis; Noise sensitivity; State-space representation; Transformations; Variable digital filter; Finite wordlength effect; Four-multiplier-lattice structure; State-space representation; Gramian-preserving frequency transformation; Variable digital filter
• ISSN: 1051-2004; 1095-4333
• DOI: 10.1016/j.dsp.2014.01.003

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.