Mathematically, if a function in the real number field can be expressed by the finite linear combination of indicator function in the semi-open interval, then this function is a step function. Step function is a combination of finite segment piecewise constant functions.

Step function is singular function, t

Extended data:

The function of step function ε(t) and test function φ(t) is to give it a numerical value, which is equal to the definite integral of φ(t) in the range of (0, ∞).

Nature:

(1) can represent some signals conveniently.

(2) The step function is used to indicate the action range of the signal.

When doing integral transformation, the original function and the image function defined by segments must be processed in segments, which is often troublesome and easy to make mistakes. Step functions can be used to represent piecewise defined functions in a unified form. Cutting the function or uniformly expressing the function defined by segments as a function defined on the integer axis often makes the transformation simple, simplifies the operation and reduces the error.

Baidu Encyclopedia-Step Function