An analogue filter synthesis package based upon vector space operations

Autor:	Thomas G. Marshall, F. C. Liu
Rok vydání:	1980
Předmět:	Polynomial Basis (linear algebra) Applied Mathematics Computer Science Applications Electronic Optical and Magnetic Materials Polynomial long division Analogue filter Filter (video) Electrical and Electronic Engineering Complex number Algorithm Change of basis Mathematics Vector space
Zdroj:	International Journal of Circuit Theory and Applications. 8:419-430
ISSN:	1097-007X 0098-9886
DOI:	10.1002/cta.4490080407
Popis:	A complete APL analogue filter synthesis package is described which includes provisions for avoiding ill-conditioning when polynomials with clustered roots are considered. The solution to the numerical problem that is employed in this package is the introduction of a change in representation in a linear manner by a change of basis. This is accomplished by the reformulation of the polynomial problem as a vector space problem. This results in a set of vector space synthesis algorithms which are conveniently implemented in APL. The conventional polynomial operations of filter synthesis such as polynomial division, zero shifting, and removal of a known factor lead to interesting and challenging vector space algorithms. These algorithms and their APL implementations are discussed. An advantage of this approach for APL implementations is that complex arithmetic can be avoided by selecting an appropriate basis for the vector space.
Databáze:	OpenAIRE
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