- #1
Manchot
- 473
- 4
I'm trying to justify to myself that the inverse Fourier transform of the Fourier transform of a function is the function itself, provided that the FT exists. I can't simplify the double integral that results when this operation is performed, and much to my dismay, nothing at Mathworld, Wikipedia, or Google has the answer. This is the integral which I'm trying to compute:
[tex] \frac{1}{2 \pi}\int_{-\infty}^{\infty}(\int_{-\infty}^{\infty}f(t) e^{-i \omega t}dt) e^{i \omega t}d{\omega} [/tex]
Is there some sort of coordinate transformation that would help me out here? I have no idea how to begin simplifying this. Thanks.
[tex] \frac{1}{2 \pi}\int_{-\infty}^{\infty}(\int_{-\infty}^{\infty}f(t) e^{-i \omega t}dt) e^{i \omega t}d{\omega} [/tex]
Is there some sort of coordinate transformation that would help me out here? I have no idea how to begin simplifying this. Thanks.