transfer function

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 output :

or

where is the transfer function of the LTI system.
In discrete-time systems, the function is similarly written as (see Z-transform) and is often referred to as the pulse-transfer function.