Transfer function refers to a mathematical representation of how a system's output is related to its input. There are various synonyms for transfer function, including system function, input-output function, and response function. Other terms that are sometimes used in place of transfer function include characteristic function, transmission function, and transfer characteristic. In the context of electrical engineering, the term transfer impedance is also sometimes used to refer to transfer functions. Regardless of the specific term used, transfer functions are a fundamental tool for analyzing and designing complex systems across a range of disciplines, from control theory and signal processing to physics and economics.