In statistical time-series analysis, signal processing and control engineering, a transfer function is a mathematical relationship between a numerical input to a dynamic system and the resulting output. The theory of transfer functions describes how the input/output relationship is affected by the structure of the transfer function. The theory of the transfer functions of linear time-invariant (LTI) systems has been available for many years. It was developed originally in connection with electrical and mechanical systems described in continuous time. The basic theory can be attributed largely to Oliver Heaviside (1850–1925)  . With the advent of digital signal processing, the emphasis has shifted to discretetime representations. These are also appropriate to problems in statistical time-series analysis, where the data are in the form of sequences of stochastic values sampled at regular intervals.
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