 Fourier representation of the Dirac delta function

ID: fourier-representation-of-the-dirac-delta-function

The identity

δ (x) = \frac{1}{2 π} \int_{- \infty}^{\infty} e^{ik x} d k

is interpreted distributionally: symmetric frequency cutoffs give

sin (n x) / (π x)

, which converge to the Dirac delta function.

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