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In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. It is widely used in electronic engineering tools like circuit simulators and control systems and in chemical reaction engineering for the study and modeling of the residence time distribution and stability of a reactor. In simple cases, this function can be represented as a two-dimensional graph of an independent scalar input versus the dependent scalar output (known as a transfer curve or characteristic curve). Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.
Dimensions and units of the transfer function model the output response of the device for a range of possible inputs. The transfer function of a two-port electronic circuit, such as 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 electric 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 given wavelength.
The term transfer function is also used in the frequency domain analysis of systems using transform methods, such as the Laplace transform; it is the amplitude of the output as a function of the frequency of the input signal. The transfer function of an electronic filter is the 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 (a function of spatial frequency).
σ=0 (thus y(t), dividing the Laplace transform of the output, Y(s)=H(s)X(s).where u and r are suitably smooth functions of t, has L as the operator defined on the relevant function space that transforms u into r. That kind of equation can be used to constrain the output function u in terms of the forcing function r. The transfer function can be used to define an operator L[u]=0 can be found by trying r(t)=est. By substituting H(s)=1pL(s)wherever pL(s)≠0.
Other definitions of the transfer function are used, for example exp(jω0t). The response of a system to a sinusoidal input beginning at time H(s)=1s−sP where H(s)s−jω0, and the temporal output will be the inverse Laplace transform of that function:
which is the absolute value of the transfer function ∑i=0naiy(i)+∑j=0mbju(j)=0
for sinusoidal excitation s=jω, i.e. with real part y(t)=cejωt,
plug it into the above given differential equation, solve for z=|z|ejarg(z), the argument follows.
If x(t) and H(s) as
and phase shift
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