`heaviside`

Heaviside step function.

Category: Mathematics > Mathematical Functions

Syntax

Y = heaviside(X)

Returns 0 for negative, 1/2 at zero and 1 for positive values.

Description

The step function switches a signal on at the origin. Shifted copies such as heaviside(t - 2) turn on at t = 2, and differences of steps build rectangular pulses. Its derivative is dirac. The value at the jump is 1/2 by default, and the choice can be changed with sympref('HeavisideAtOrigin', value).

Input arguments

X: Numeric or symbolic array (real).

Output arguments

Y: Array of the same size. For a symbolic X the call heaviside(x) stays unevaluated.

Example

Step and rectangular pulse

heaviside([-2 0 3])
t = -1:4;
heaviside(t - 1) - heaviside(t - 3)

Output

ans = 1×3

         0    0.5000    1.0000
ans = 1×6

         0         0    0.5000    1.0000    0.5000         0

See also

dirac sign laplace piecewise sympref