Explanation
Transfer functions are commonly used in the analysis of systems such as single-input single-output filters, typically within the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear, time-invariant systems (LTI), as covered in this article. Most real systems have non-linear input/output characteristics, but many systems, when operated within nominal parameters (not "over-driven") have behavior that is close enough to linear that LTI system theory is an acceptable representation of the input/output behavior.
In its simplest form for continuous-time input signal and output, the transfer function is the linear mapping of the Laplace transform of the input, to the Laplace transform of the output :
or
In discrete-time systems, the function is similarly written as (see Z-transform) and is often referred to as the pulse-transfer function.
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