论文信息 - Gramian-preserving frequency transformation for linear discrete-time systems using normalized lattice structure

Gramian-preserving frequency transformation for linear discrete-time systems using normalized lattice structure

This paper presents a new algorithm for realization of Gramian-preserving frequency transformation for linear discrete-time systems. In the proposed algorithm, we construct allpass systems for frequency transformation as the cascaded normalized lattice structure. It is shown that the frequency transformation based on this algorithm not only leaves the controllability/observability Gramians invariant under the change of magnitude responses, but also significantly reduces nonzero entries of the coefficient matrices of transformed systems. This property will be very effective in practical applications such as implementation of high-accuracy multiband state-space digital Alters.

Shunsuke Koshita | Masayuki Kawamata | Masahide Abe | Satoru Tanaka

[1] R. Roberts,et al. Roundoff noise in digital filters: Frequency transformations and invariants , 1976 .

[2] Shunsuke Koshita,et al. Gramian-Preserving Frequency Transformation for State-Space Digital Filters , 2006, APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems.

[3] S. Hwang. Minimum uncorrelated unit noise in state-space digital filtering , 1977 .

[4] Robert Bregovic,et al. Multirate Systems and Filter Banks , 2002 .

[5] M. Kawamata,et al. On the absence of limit cycles in a class of state-space digital filters which contains minimum noise realizations , 1984 .

[6] B. Moore. Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[7] Anthony G. Constantinides,et al. Spectral Transformations for Digital Filters , 1970 .

[8] Clifford T. Mullis,et al. Synthesis of minimum roundoff noise fixed point digital filters , 1976 .

[9] Shunsuke Koshita,et al. Gramian-preserving frequency transformation for linear continuous-time state-space systems , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[10] Masayuki Kawamata,et al. A unified approach to the optimal synthesis of fixed-point state-space digital filters , 1985, IEEE Trans. Acoust. Speech Signal Process..