Transfer function

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.

Background

Take a complex harmonic signal with a sinusoidal component with amplitude A_in, angular frequency ω and phase p_in

x(t) = A_in * exp(j * (ωt + p_in))

(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) = A_out * exp(j * (ωt + p_out)).

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

'Gain',

A_out/A_in = | H(jω) |

and 'Phase shift'

p_out - p_in = arg( H(jω) ).

---

/Talk