ABSTRACT
Transfer-function models (strictly, Laplace transfer-functions) are based on the Laplace transform, and are versatile means of representing linear systems with constant (time-invariant) parameters. Strictly, these are dynamic models in the Laplace domain. Frequency-domain models (or frequency transfer-functions) are a special category of Laplace domain models, and they are based on the Fourier transform. However, they are interchangeable-a Laplace domain model can be converted into the corresponding frequency domain model in a trivial manner, and vice versa. Similarly linear, constantcoefficient (time-invariant) time-domain model (e.g., input-output differential equation or a state-space model) can be converted into a transfer-function, and vice versa, in a simple and straightforward manner. A system with just one input (excitation) and one output (response) can be represented uniquely by one transfer-function. When a system has two or more inputs (i.e., an input vector) and/or two or more outputs (i.e., and output vector), its representation needs several transfer-functions (i.e., a transfer-function matrix is needed). The response characteristics at a given location (more correctly, in a given degree of freedom) can be determined using a single frequency-domain transfer-function.
