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?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Difference between Forward and Backward Fourier Transforms?

Loading...

Similar Threads - Difference between Forward | Date |
---|---|

I Difference Between d3x and triple Integral | Sep 24, 2017 |

B Difference between integral and a function | Jan 22, 2017 |

I What is the difference between these two approaches? | Dec 15, 2016 |

I What is the difference between dx, Δx and δx? | Jul 24, 2016 |

I Difference between integral and antiderivative? | Apr 19, 2016 |

**Physics Forums - The Fusion of Science and Community**