Symbolic Math Toolbox™

dirac - Dirac delta

Syntax

dirac(x)

Description

dirac(x) returns the Dirac delta function of x.

The Dirac delta function, dirac, has the value 0 for all x not equal to 0 and the value Inf for x = 0. Several Symbolic Math Toolbox™ functions return answers in terms of dirac.

dirac has the property that

int(dirac(x-a)*f(x),-inf,inf) = f(a)

for any function f and real number a. It also has the following relationship to the function heaviside:

diff(heaviside(x),x)
 
ans =
 
dirac(x)

Example

syms x a
a = 5;
int(dirac(x-a)*sin(x),-inf, inf)
 
ans =
 
sin(5)

See Also

heaviside

digits

double