A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. It is mainly used in (digital) signal processing.
Take a complex harmonic signal with a sinusoidal component with amplitude Ain, angular frequency ω and phase pin
- x(t) = Ain * exp(j * (ωt + pin))
(where j represents the imaginary unit) and use it as an input to a linear time-invariant system. The corresponding component in the output will match the following equation:
- y(t) = Aout * exp(j * (ωt + pout)).
Note that the fundamental frequency ω has not changed, only the amplitude and the phase of the response changed as it went through the system. The transfer function H(z) describes this change for every frequency ω in terms of
- Aout/Ain = | H(jω) |
and 'Phase shift'
- pout - pin = arg( H(jω) ).