Explanation
Transfer functions are commonly used in the analysis of systems such as single-input single-output filters, typically within the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear, time-invariant systems (LTI), as covered in this article. Most real systems have non-linear input/output characteristics, but many systems, when operated within nominal parameters (not "over-driven") have behavior that is close enough to linear that LTI system theory is an acceptable representation of the input/output behavior.
In its simplest form for continuous-time input signal and output, the transfer function is the linear mapping of the Laplace transform of the input, to the Laplace transform of the output :
or
In discrete-time systems, the function is similarly written as (see Z-transform) and is often referred to as the pulse-transfer function.
Read more about this topic: Transfer Function
Famous quotes containing the word explanation:
“There is a great deal of unmapped country within us which would have to be taken into account in an explanation of our gusts and storms.”
—George Eliot [Mary Ann (or Marian)
“What causes adolescents to rebel is not the assertion of authority but the arbitrary use of power, with little explanation of the rules and no involvement in decision-making. . . . Involving the adolescent in decisions doesn’t mean that you are giving up your authority. It means acknowledging that the teenager is growing up and has the right to participate in decisions that affect his or her life.”
—Laurence Steinberg (20th century)
“We live between two worlds; we soar in the atmosphere; we creep upon the soil; we have the aspirations of creators and the propensities of quadrupeds. There can be but one explanation of this fact. We are passing from the animal into a higher form, and the drama of this planet is in its second act.”
—W. Winwood Reade (1838–1875)