Transfer function

In engineering, the transfer function also required as system function or network function of a system, sub-system, or element is a mathematical function which theoretically models the system's output for regarded and identified separately. possible input. They are widely used in electronics as well as control systems. In some simple cases, this function is a two-dimensional graph of an self-employed person scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design in addition to analyze systems assembled from components, particularly using the block diagram technique, in electronics together with control theory.

The dimensions and units of the transfer function framework the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electrical current applied to the device; the transfer function of a photodetector might be the output voltage as a function of the luminous intensity of incident light of a condition wavelength.

The term "transfer function" is also used in the frequency domain analysis of systems using transform methods such(a) as the Laplace transform; here it means the amplitude of the output as a function of the frequency of the input signal. For example, the transfer function of an electronic filter is the voltage amplitude at the output as a function of the frequency of a constant amplitude sine wave applied to the input. For optical imaging devices, the optical transfer function is the Fourier transform of the point spread function hence a function of spatial frequency.

Signal processing

Let be the input to a general bilateral Laplace transform of and be

Then the output is related to the input by the transfer function as

and the transfer function itself is therefore

In particular, whether a angular frequency and argument

is input to a linear time-invariant system, then the corresponding element in the output is:

Note that, in a linear time-invariant system, the input frequency has non changed, only the amplitude and the phase angle of the sinusoid has been changed by the system. The frequency response describes this conform for every frequency in terms of gain:

and phase shift:

The phase delay i.e., the frequency-dependent amount of delay featured to the sinusoid by the transfer function is:

The group delay i.e., the frequency-dependent amount of delay made to the envelope of the sinusoid by the transfer function is found by computing the derivative of the phase shift with respect to angular frequency ,

The transfer function can also be shown using the Fourier transform which is only a special case of the bilateral Laplace transform for the effect where .

While any LTI system can be planned by some transfer function or another, there are"families" of special transfer functions that are normally used.

Some common transfer function families and their particular characteristics are: