Rational Decomposition Research Articles

Decompositions of Localized Fibres and Cofibres

AbstractIn this paper p-local versions of the Rational Fibre and Cofibre Decomposition Theorems are given. In particular, if there exists an element in the nth Gottlieb group of a space F such that its image under the Hurewicz map has infinite order, then Sn for almost all primes p. A dual result is proved for cofibrations.

Additive and multiplicative minimum-phase decompositions of 2-D rational power density spectra

This paper considers the multiplicative and additive minimum-phase decompositions of a two-dimensional (2-D) rational power density spectrum (commonly known as the spectral factorization and partial fraction expansion problems). It is shown that both of these decompositions generally involve filters which are ratios of 2-D minimum-phase filters, with finite support in one variable, and infinite support in the other variable. It is shown that a sufficient condition for a 2-D autoregressive (AR) spectrum to have a rational additive decomposition is for the minimum-phase whitening filter to have finite reflection coefficient support.

Another Proof of the Rational Decomposition Theorem

Another Proof of the Rational Decomposition Theorem

Another Proof of the Rational Decomposition Theorem

Another Proof of the Rational Decomposition Theorem

New methods of rational function decomposition with applications in active network synthesis†

With the growing importance of active RC synthesis, it has become necessary to decompose a given rational function in a certain manner. In this paper three new methods of decomposition of a real rational function with no restriction on the numerator order, relative to the denominator order, are presented and their applications illustrated