Dirac Delta Function

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Dirac Function[edit]

Definition[edit]

The Dirac function is a "signal" with unit energy that is concentrated around


Alternative definition[edit]

This is a gaussian distribution with spread 0.

Properties[edit]

Energy[edit]


NB: has no mathematical meaning, as isn't an ordinary function but a distribution. The special nature of appears clearly e.g. when you try to square the same Gaussian distribution above and try to compute the same limit of the integral in . The result will be quite surprising: it is !

Convolution[edit]

Kronecker Delta Function[edit]

The Kronecker delta function is the discrete analog of the Dirac function. It has Energy 1 and only a contribution at

Properties[edit]

Energy[edit]

Convolution[edit]