These functions give the relation between the input and the output of a linear, time invariant system. A frequency response is found in the form of a ratio of two polynoms:
The zeros of the numerator are called the zeroes of the transfer function. The zeros of the denominator are called the poles of the transfer function. Both zeroes and poles are either real or complex conjugates.
The transfer function of a system with only complex conjugate zeroes, and , and poles and , can be written as:
If there is a real zero, , and a real pole, , the transfer function becomes:
The frequency response is usually represented as a combination of two plots: the amplitude response and the phase response.