Rational approximation of frequency domain responses in the S and Z planes

2005 ◽  
Author(s):  
A.C.S. Lima ◽  
A.B. Fernandes ◽  
S. Carneiro
Keyword(s):  
Frequency Domain ◽  
Rational Approximation

scholarly journals Rational Implementation of Fractional Calculus Operator Based on Quadratic Programming

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhisong Xu ◽  
Mingqiu Li
Keyword(s):  
Fractional Calculus ◽  
Quadratic Programming ◽  
Frequency Domain ◽  
Frequency Band ◽  
Rational Approximation ◽  
Least Squares Method ◽  
Approximation Accuracy ◽  
Approximation Function ◽  
Fractional Calculus Operators ◽  
Quadratic Programming Method

When fractional calculus operators and models are implemented rationally, there exist some problems such as low approximation accuracy of rational approximation function, inability to specify arbitrary approximation frequency band, or poor robustness. Based on the error criterion of the least squares method, a quadratic programming method based on the frequency-domain error is proposed. In this method, the frequency-domain error minimization between the fractional operator s ± r and its rational approximation function is transformed into a quadratic programming problem. The results show that the construction method of the optimal rational approximation function of fractional calculus operator is effective, and the optimal rational approximation function constructed can effectively approximate the fractional calculus operator and model for the specified approximation frequency band.

Advancements in Iterative Methods for Rational Approximation in the Frequency Domain

2007 ◽  
Vol 22 (3) ◽  
pp. 1633-1642 ◽  
Author(s):  
Dirk Deschrijver ◽  
Bjrn Gustavsen ◽  
Tom Dhaene
Keyword(s):  
Frequency Domain ◽  
Iterative Methods ◽  
Rational Approximation
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