Dirac Delta Function
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Dirac Function[edit | edit source]
Definition[edit | edit source]
The Dirac function is a "signal" with unit energy that is concentrated around
Alternative definition[edit | edit source]
This is a gaussian distribution with spread 0.
Properties[edit | edit source]
Energy[edit | edit source]
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 | edit source]
Kronecker Delta Function[edit | edit source]
The Kronecker delta function is the discrete analog of the Dirac function. It has Energy 1 and only a contribution at