*Kiddle Encyclopedia.*

The **Heaviside function**, *H* is a non-continuous function whose value is zero for negative argument and one for positive argument.

The function is used in the mathematics of control theory to represent a signal that switches on at a specified time and stays switched on indefinitely. It was named after the Englishman Oliver Heaviside.

The Heaviside function is the integral of the Dirac delta function: *H*′ = *δ*. This is sometimes written as

## Contents

## Discrete form

We can also define an alternative form of the Heaviside step function as a function of a discrete variable *n*:

where *n* is an integer.

Or

The discrete-time unit impulse is the first difference of the discrete-time step

This function is the cumulative summation of the Kronecker delta:

where

is the discrete unit impulse function.

## Representations

Often an integral representation of the Heaviside step function is useful:

*H*(0)

The value of the function at 0 can be defined as *H*(0) = 0, *H*(0) = ½ or *H*(0) = 1.