A transfer function is a mathematical representation used in control theory and signal processing to describe the relationship between the input and output of a linear time-invariant (LTI) system in the frequency domain. It is typically expressed as a ratio of two polynomials.
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For a linear time-invariant system with zero initial data, the transfer function is the Laplace-domain ratio . A rational causal system is BIBO stable when all poles lie in the open left half-plane.