Realization of general extended state-space fixed-point digital filters with minimum roundoff noise

Author

Keith Marlin Anspach

Date of Award

8-1994

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Bruce W. Bomar

Committee Members

John E. Caruthers, Remi C. Engels, Roy D. Joseph

Abstract

In this study a technique for determining a minimum roundoff noise extended state-space (e-state) realization of fixed-point recursive digital filters is developed. Previous efforts developed such e-state structures for the second order e-state equa- tion only. This new algorithm determines a minimum roundoff e-state structure for the general order e-state equation. The technique determines a linear transforma- tion which changes the original structure into an e-state structure with minimum roundoff noise. A combination of a conjugate gradient algorithm and a variable metric algorithm is employed to determine the linear transformation. The roundoff noise characteristics of e-state structures are investigated by studying numerical examples. It is found that the minimum noise e-state structure can have lower roundoff noise than the conventional minimum noise structure, since fewer state variables are actually computed. In an e-state structure, an N_th order filter where N = LM can be implemented by M difference equations of order L resulting in a computational complexity of O[L(M+1)²]. Compared to other realizations, the e- state structure uses fewer, but longer inner products which pipelined digital signal processors are designed to handle very efficiently.

Recommended Citation

Anspach, Keith Marlin, "Realization of general extended state-space fixed-point digital filters with minimum roundoff noise. " PhD diss., University of Tennessee, 1994.
https://trace.tennessee.edu/utk_graddiss/10288