What is the difference between forward and backward Fourier transforms? I'm look:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

F(k) = \int_{-\infty}^{\infty} f(x)\ e^{- i 2\pi k x }\,dx

[/tex]

[tex]

f(x) = \int_{-\infty}^{\infty} F(k)\ e^{ i 2\pi k x }\,dk

[/tex]

If I swap the x and the k in the second equation, the transforms are then:

[tex]

F(k) = \int_{-\infty}^{\infty} f(x)\ e^{- i 2\pi k x }\,dx

[/tex]

[tex]

F(k) = \int_{-\infty}^{\infty} f(x)\ e^{ i 2\pi x k }\,dx

[/tex]

and the only difference is the minus sign in the exponent. What gives? Why aren't the forward and backwards transforms identical?

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# Difference between Forward and Backward Fourier Transforms?

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