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 and control theory.
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2 Signal Processing 3 Control Engineering |
Take a complex harmonic signal with a sinusoidal component with amplitude , angular frequency and phase
Background
Signal Processing
(where i 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:
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 transfer function can also be derived by using the Fourier transform.
In control engineering and control theory the transfer function is derived using the Laplace transform.Control Engineering