Sensitivity analysis of digital filter structures

A coefficient sensitivity measure for state space recursive, finite wordlength, digital filters is developed and its relationship to the filter output quantization noise power is derived. The sensitivity measure is simply the sum of the L₂ norm of all first order partials of the system function with respect to the system parameters; alternatively, the measure may be viewed as the output variance of the error system created by the inherent parameter quantization. Since the measure uses only the first order partials, it is a lower bound approximation to the output quantization noise power. During analysis, numerically unstable conditions may occur because ideal filter characteristics imply system poles which are almost on the unit circle in the z-plane; therefore, it is proposed to scale the radii of the pole and zero magnitudes. Thus, the scaled system has the same frequency information as the original system, but performs better numerically. The direct II form sensitivity, which is shown to be inversely proportional to the product of the system pole and zero distances, can be reduced by the judicious placement of added pole/zero cancellation pairs which increase the order of the system but do not change the system function.

Name thesis:degree_name

M. Eng.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Electrical Engineering

Department dc:contributor.department

Electrical Engineering

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1986

Author dc:creator

• DeBrunner, Victor Earl

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/104319

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/104319