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
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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