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In my book the dirac delta is described by the equation on the attached picture. This realtion is derived from the Fourier transform, but I'm not sure that I understand what it says. If u=t it is clear that one gets f(u) in the Fourier inversion theorem. But why wouldn't u=t? In the derivation of the Fourier transform from the discrete Fourier series t was just changed to u in the expression of the coefficients to avoid confusion.
Can anyone try to picture what this expression fundamentally says? I should suspect that it is like the analogue of the ortogonality relation of the discrete Fourier series, but I can't quite understand it.
And what would the situation u≠t represent?
Can anyone try to picture what this expression fundamentally says? I should suspect that it is like the analogue of the ortogonality relation of the discrete Fourier series, but I can't quite understand it.
And what would the situation u≠t represent?