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Complex Variables
Published in William S. Levine, Control System Fundamentals, 2019
We shall assume in the discussion that the quotient is in reduced form and there are no common factors and hence no common zeros. A rational function is called proper if m ≤ n. If the degrees satisfy m < n, then H(z) is called strictly proper. In control engineering, rational functions most commonly occur as the transfer functions of linear systems. Rational functions H(z) of a variable z denote the transfer functions of discrete systems and transfer functions H(s) of the variable s are employed for continuous systems. Strictly proper functions have the property that limz→∞H(z)=0
Complex Variables
Published in William S. Levine, The Control Handbook: Control System Fundamentals, 2017
We shall assume in the discussion that the quotient is in reduced form and there are no common factors and hence no common zeros. A rational function is called proper if m ≤ n. If the degrees satisfy m < n, then H(z) is called strictly proper. In control engineering, rational functions most commonly occur as the transfer functions of linear systems. Rational functions H(z) of a variable z denote the transfer functions of discrete systems and transfer functions H(s) of the variable s are employed for continuous systems. Strictly proper functions have the property that
Other Power Amplifier Modeling
Published in Jingchang Nan, Mingming Gao, Nonlinear Modeling Analysis and Predistortion Algorithm Research of Radio Frequency Power Amplifiers, 2021
The rational function is defined as a ratio of two power polynomials y(n)=a0+a1x(n)+⋯+aJxJ(n)b0+b1x(n)+⋯+bKxK(n)=∑i=0Jaixi(n)∑j=0Kbjxj(n)where x(n) and y(n) denote the input and output of the rational function at moment n, respectively.
The extension of the linear inequality method for generalized rational Chebyshev approximation to approximation by general quasilinear functions
Published in Optimization, 2022
Vinesha Peiris, Nadezda Sukhorukova
The rational function is defined to be a ratio of two polynomials. Most prominent methods (Remez method, differential correction method, linear inequality method, etc.) developed for uniform rational approximation were originally defined for the ratio of polynomials. Some of them (e.g. linear inequality and differential correction) were extended to generalized rational Chebyshev approximation (ratios of linear functions with respect to its decision variables, introduced in [26]).