I am reading a Fourier Transform definition in two places, in the first is
$\int_{-\infty}^{\infty}f(x)\exp(-ijw)dx$
and another is
$\int_{-\infty}^{\infty}f(x)\exp(-2\pi ijw)dx$
I want know Why the first is without $(2\pi)$?.
I am reading a Fourier Transform definition in two places, in the first is
$\int_{-\infty}^{\infty}f(x)\exp(-ijw)dx$
and another is
$\int_{-\infty}^{\infty}f(x)\exp(-2\pi ijw)dx$
I want know Why the first is without $(2\pi)$?.
You will find many different expressions for the Fourier transform $\hat f_{a,b}(\omega) = \frac{b}{\sqrt{2\pi}}\int_{-\infty}^\infty f(x) e^{-i a x \omega}\,dx$ with $a,b\in \mathbb{R}$.
The different Fourier transform obey the relation $\hat f_{a,b}(\omega) = b \hat f_{1,1}(a \omega)$ so they essentially all have the same information.
They're essentially equivalent - the only difference is a rescaling of $x$. They both lead to Fourier transforms which differ by a multiplicative constant, and so as long as the definition of the inverse Fourier transform is consistent with your choice, it doesn't matter.