Dirac Delta Function
aka delta function, Dirac delta distribution, δ distribution, unit impulse
definition \(\delta = \lim g\ 0\), where \(g\) is the gaussian function --- Wikipedia
definition \(\int_{-\infty}^\infty \delta = 1 \land \int_{-\infty}^\infty g\delta = g\ 0\), for any well-behaved function \(g\) --- Wikipedia
properties
integral \(\int_{-\infty}^\infty \delta = 1\)
identity of convolution \(\delta \ast f = f\)
fourier transform \(\mathcal F\ \delta = x.\ 1\)
y-intercept \(\delta\ 0 = \infty\)
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--- https://en.wikipedia.org/wiki/Dirac_delta_function#Fourier_transform
--- https://stackoverflow.com/questions/5824704/what-is-the-do-nothing-convolution-kernel