The Heaviside step function, or the unit step function, usually denoted by H (but sometimes u or θ), is a discontinuous function whose value is zero for negative argument and one for positive argument. It seldom matters what value is used for H(0), since H is mostly used as a distribution. Some common choices can be seen below.
The function is used in the mathematics of control theory and signal processing to represent a signal that switches on at a specified time and stays switched on indefinitely. It is also used in structural mechanics together with the Dirac delta function to describe different types of structural loads. It was named after the English polymath Oliver Heaviside.
It is the cumulative distribution function of a random variable which is almost surely 0. (See constant random variable.)
The Heaviside function is the integral of the Dirac delta function: H′ = δ. This is sometimes written as
although this expansion may not hold (or even make sense) for x = 0, depending on which formalism one uses to give meaning to integrals involving δ.
Read more about Heaviside Step Function: Discrete Form, Analytic Approximations, Integral Representations, Zero Argument, Antiderivative and Derivative, Fourier Transform, Algebraic Representation, Hyperfunction Representation
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