
A new Z domain continued fraction expansion is presented which proceeds in terms of z - 1 and 1 - z^{-1} factors. It is proved to be always convergent for polynomials whose roots all lie within the unit circle. The procedure involves a unique decomposition of the given polynomial into a mirror image polynomial (MIP) and an antimirror image polynomial (AMIP) whose degrees differ by unity. The ratio of these polynomials is shown to possess the properties of a digital reactance function. The continued fraction expansion developed here-due to the fact that z - 1 and 1 - z^{-1} are the inverse transmittances of digital accumulators, as well as of switched capacitor integrators-has application to the synthesis of digital and switched capacitor ladder filters.
Transformations, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Stability of control systems, continued fraction expansion, image polynomial, Polynomials and rational functions of one complex variable, Analytic circuit theory, digital reactance function
Transformations, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Stability of control systems, continued fraction expansion, image polynomial, Polynomials and rational functions of one complex variable, Analytic circuit theory, digital reactance function
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 40 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
