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In [[control theory]], a '''proper transfer function''' is a [[transfer function]] in which the [[Degree of a polynomial|degree]] of the numerator does not exceed the degree of the denominator. A '''strictly proper'''
The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the ''relative degree'' of the transfer function.
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because
:<math> \deg(\textbf{N}(s)) = 4 \nleq \deg(\textbf{D}(s)) = 3 </math>.
A '''not proper''' transfer function can be made proper by using the method of long division.
The following transfer function is '''strictly proper'''
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==References==
* [https://web.archive.org/web/20160304220240/https://courses.engr.illinois.edu/ece486/documents/set5.pdf Transfer functions] - ECE 486: Control Systems Spring 2015, University of Illinois
* [http://www.ece.mcmaster.ca/~ibruce/courses/EE4CL4_lecture9.pdf ELEC ENG 4CL4: Control System Design Notes for Lecture #9], 2004, Dr. Ian C. Bruce, McMaster University
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