Editing Transfer function (section)

{{Short description|Function specifying the behavior of a component in an electronic or control system}}
{{distinguish|Transformation (function)}}

In [[engineering]], a '''transfer function''' (also known as '''system function'''<ref>[[Bernd Girod]], Rudolf Rabenstein, Alexander Stenger, ''Signals and systems'', 2nd ed., Wiley, 2001, {{ISBN|0-471-98800-6}} p. 50</ref> or '''network function''') of a system, sub-system, or component is a [[function (mathematics)|mathematical function]] that [[mathematical model|models]] the system's output for each possible input.<ref name="LaughtonWarne2002">{{cite book|author1=M. A. Laughton|author2=D.F. Warne|title=Electrical Engineer's Reference Book|date=27 September 2002|publisher=Newnes|isbn=978-0-08-052354-5|pages=14/9–14/10|edition=16}}</ref><ref name="Parr1993">{{cite book|author=E. A. Parr|title=Logic Designer's Handbook: Circuits and Systems|year=1993|publisher=Newness|isbn=978-1-4832-9280-9|pages=65–66|edition=2nd}}</ref><ref name="SinclairDunton2007">{{cite book|author1=Ian Sinclair|author2=John Dunton|title=Electronic and Electrical Servicing: Consumer and Commercial Electronics|year=2007|publisher=Routledge|isbn=978-0-7506-6988-7|page=172}}</ref> It is widely used in [[electronic engineering]] tools like [[Electronic circuit simulation|circuit simulators]] and [[control system]]s. In simple cases, this function can be represented as a two-dimensional [[graph (function)|graph]] of an independent [[scalar (mathematics)|scalar]] input versus the dependent scalar output (known as a '''transfer curve''' or '''characteristic curve'''). Transfer functions for components are used to design and analyze systems assembled from components, particularly using the [[block diagram]] technique, in electronics and [[control theory]].

Dimensions and units of the transfer function model the output response of the device for a range of possible inputs. The transfer function of a [[two-port]] electronic circuit, such as an [[amplifier]], might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical [[actuator]] might be the mechanical displacement of the movable arm as a function of electric current applied to the device; the transfer function of a [[photodetector]] might be the output voltage as a function of the [[luminous intensity]] of incident light of a given [[wavelength]].

The term "transfer function" is also used in the [[frequency domain]] analysis of systems using transform methods, such as the [[Laplace transform]]; it is the [[amplitude]] of the output as a function of the [[frequency]] of the input signal. The transfer function of an [[electronic filter]] is the amplitude at the output as a function of the frequency of a constant amplitude [[sine wave]] applied to the input. For optical imaging devices, the [[optical transfer function]] is the [[Fourier transform]] of the [[point spread function]] (a function of [[spatial frequency]]).