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

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 L2L2-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.