The fourier transform, wrt to angular frequency, needs of a factor (1/2π) for get f(t) or F(ω), actually, this factor is broken in 2 factors (1/√2pi) and each kernel, direct and inverse, receives one factor for keep the symmetry in equation.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]F(\omega)=\int_{-\infty }^{+\infty }\frac{e^{-i\omega t}}{\sqrt{2\pi}} f(t)dt[/tex]

[tex]f(t)=\int_{-\infty }^{+\infty }\frac{e^{+i\omega t}}{\sqrt{2\pi}} F(\omega)d\omega[/tex]

Why others transform, by definition, don't have its "conversion factor" "broken" in 2 and distributed in each kernel? Is wrong define the transforms in this way? Prejudice the calculus?

**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!

# Integral tranforms and symmetry

Loading...

Similar Threads - Integral tranforms symmetry | Date |
---|---|

B Calculate the expression of the antiderivative | Feb 19, 2018 |

A Newmark-Beta vs Predictor Corrector | Jan 4, 2018 |

A Can Newton's method work with an approximated integral | Dec 28, 2017 |

I Three different integration schemes | Oct 25, 2017 |

Laplace tranform on functions | Sep 4, 2009 |

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