# Plot a Dirac Delta Function?

Posted 4 months ago
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 Good Evening All, I have stumbled across a Dirac Delta Function, when applying the Fourier Transform to a function. I am not quite sure how to plot it. Could anyone provide some guidance? Thanks! F[t_] := A*Sin[ t] g[k_] := FourierTransform[F[t], t, k] I A Sqrt[\[Pi]/2] DiracDelta[-1 + k] - I A Sqrt[\[Pi]/2] DiracDelta[1 + k 
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Posted 4 months ago
 It's really a functional, not a function. There is no reason to expect one could "plot" it in the usual sense.
Posted 4 months ago
 Delta Function is a generalized function, not a functional bud. But thanks anyways
Posted 4 months ago
 Check the part about linear functionals.
Posted 4 months ago
 You can approximate it. Plot[PDF[NormalDistribution[0, 10^-2], x], {x, -2, 2}, PlotRange -> {0, 1}] 
Posted 4 months ago
 That’s it! Thanks! It’s undefined at zero so we gotta approximate, makes sense. Thanks!!
Posted 4 months ago
 To be honest, I would be quite unhappy if a plot of DiracDelta would actually show anything! What you can do is making something visible by showing its convolution with some "sharp" function, e.g.: f[t_] := a Sin[t] g[\[FormalK]_] = FourierTransform[f[\[FormalT]], \[FormalT], \[FormalK]]; plotDelta[f_, k_] := Total@*ReIm@Convolve[f[\[FormalX]], HeavisideLambda[50 \[FormalX]], \[FormalX], k] Plot[Evaluate[plotDelta[g, k] /. a -> 1], {k, -2, 2}, PlotRange -> All] which gives:
 The Dirac delta function is a Monster. It must be kept in a cage, called an integrand. Outside the cage, it makes no more sense than the Jabberwock. Inside the cage it may be tamed: Integrate[DiracDelta[x - a] f[x], {x, -Infinity, Infinity}, Assumptions -> Element[a, Reals]] (* f[a] *)