Angular frequency ($\omega$)

The variable $\omega$ a Fourier transform is a function of, in radians per unit time.

In $\hat f(\omega)$ , $\omega$ is called angular frequency, measured in radians per unit time rather than cycles per unit time. This course places the factor of $2\pi$ entirely on the inverse transform rather than splitting it symmetrically or folding it into the forward transform -- a convention choice, not a universal law.

Examples

A signal oscillating at ordinary frequency $f$ Hz has angular frequency $\omega=2\pi f$ radians per second.