New second-order state-space structures for realizing low-roundoff-noise digital filters with reduced number of multiplies

Author

Kian-Joo Low

Date of Award

6-1984

Degree Type

Thesis

Degree Name

Master of Science

Major

Electrical Engineering

Major Professor

R. W. Rochelle

Committee Members

B. W. Bomar, H. P. Neff

Abstract

Efficient computational algorithms for realizing high-order digital filters can be constructed around parallel-of-subfilter or cascade-of-subfilter realizations, where each subfilter is either first or second-order. To this end, several new second-order state-space digital filter structures are developed and introduced. They are then analyzed with respect to their fixed-point-arithmetic roundoff noise performance. It is found by appropriately choosing from the new structures, nth-order realizations with low roundoff noise and only about 3n multiplies are possible. This compares favorably to the 4n multiplies required by minimum-noise or normal subfilters and to the (n+1)² multiplies required by an nth-order minimum-noise structure.

Design equations are developed for each of the new structures, These equations require only algebraic, real-arithmetic calculations and give designs with inherent ℓ₂ -norm probability-of-overflow scaling. Numerical examples are included to illustrate the design of filters using the new structures and a software realization is provided to demonstrate the advantages of the new structures.

Recommended Citation

Low, Kian-Joo, "New second-order state-space structures for realizing low-roundoff-noise digital filters with reduced number of multiplies. " Master's Thesis, University of Tennessee, 1984.
https://trace.tennessee.edu/utk_gradthes/14658