Consider the following convention for defining the Fourier transform
ˆf(ω)=∫f(x)e−2πixωdω.
Why is the Fourier transform of 1 equal to δ(ω). Loosely, I see that when ω≠0 the integral will be zero and when ω=0 the integral diverges but does anyone have a more rigorous way of showing this? Also, how do we know there is not some scaling factor in front or something?
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