Online Encyclopedia
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 signal processing and control theory.
1 Signal processing
2 Control engineering
3 See also
Contents |
Background
Signal processing
Take a complex harmonic signal with a sinusoidal component with amplitude A_{in}, angular frequency ω and phase p_{in}
(where i is 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:
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:
and phase shift:
- .
The group delay (i.e., the frequency-dependent amount of delay introduced by the transfer function) is found by taking the radial frequency derivative of the phase shift,
- .
The transfer function can also be derived by using the Fourier transform.
Control engineering
In control engineering and control theory the transfer function is derived using the Laplace transform.