Transfer function

In engineering, a transfer function (also known as system function or network function and, when plotted as a graph, transfer curve) is a mathematical representation for fit or to describe inputs and outputs of black box models.

Typically it is a representation in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant (LTI) system with zero initial conditions and zero-point equilibrium. For optical imaging devices, for example, the optical transfer function is the Fourier transform of the point spread function (hence a function of spatial frequency) i.e., the intensity distribution caused by a point object in the field of view. A number of sources however use "transfer function" to mean some input-output characteristic in direct physical measures (e.g., output voltage as a function of input voltage of a two-port network) rather than its transform to the s-plane.

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 (LTI) systems, 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.

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