In engineering, a transfer function (also known as the 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 system (LTI) with zero initial conditions and zero-point equilibrium. With optical imaging devices, for example, it 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.