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Signum function
In mathematics and especially in computer science, the sign function is a logical function which extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function. The sign
function is often represented as sgn and can be defined thus:
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Any real number can be expressed as the product of its absolute
value and its sign function:
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From equation (1) it follows that
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but equation (2) is indeterminate when x is set to zero.
The signum function is the derivative of the absolute value function (up to
the indeterminacy at zero):
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Also, the derivative of the signum function is two times the Dirac delta function,
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The signum function is related to the Heaviside step
function h0.5(x) thus
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where the 0.5 subscript of the step function means that h0.5(0) = 0.5.
Also, if the step function h0(x) is thought of as a mathematical switch, with h0(x) = 0, then the signum function can be expressed as
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See also
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