The Fourier transform equations

The following equations[2,1] are valid for a Fourier transform of a signal $ f(t)$ over a finite period $ [-T,T]$.

Forward FT:

$\displaystyle F(n) = a_n - ib_n = \frac{1}{2T} \int_{-T}^{T} f(t) e^{-i n \omega t}
$

Inverse FT:

$\displaystyle f(t) = \frac{1}{2} \sum_{-\infty}^{\infty} F(n) e^{i n \omega t}
$



Bjørn Alsberg 2005-02-18