Built-in Mathematica Symbol

UnitStep

UnitStep[x]
represents the unit step function, equal to 0 for

and 1 for

.

UnitStep[x₁, x₂, ...]
represents the multidimensional unit step function which is 1 only if none of the

are negative.

MORE INFORMATION

Some transformations are done automatically when UnitStep appears in a product of terms.

UnitStep provides a convenient way to represent piecewise continuous functions.

UnitStep has attribute Orderless.

For exact numeric quantities, UnitStep internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.

UnitStep[] is 1.

EXAMPLES

CLOSE ALL

Basic Examples (3)

Evaluate numerically:

Use UnitStep to construct piecewise functions:

Evaluate numerically:

Use UnitStep to construct piecewise functions:

In[1]:=

Out[1]=

Scope (4)

The precision of the output does not track the precision of the input:

UnitStep threads element-wise over lists:

UnitStep can deal with real-valued intervals:

TraditionalForm formatting:

Generalizations & Extensions (1)

Multidimensional UnitStep:

Applications (6)

Generate a square wave:

Compute a step response for a continuous-time system:

Using transform methods:

Compute a step response for a discrete-time system:

Using transform methods:

Solve the time-independent Schrödinger equation with piecewise analytic potential:

This gives the probability of the random variable being in the interval

:

Here is the resulting probability plotted:

Construct the Walsh function:

Properties & Relations (3)

Expand into UnitStep of linear factors:

Convert into Piecewise:

Integrate over finite and infinite domains:

Possible Issues (3)

Symbolic preprocessing of functions containing UnitStep can be time-consuming:

Limit does not give UnitStep as a limit of smooth functions:

Differentiating Abs does not yield UnitStep: