# Units of FFT frequency

I'm having some trouble understanding FFT plots and measures.

According to this, this will give me the magnitude plot of FFT, but I want the area under from 1 to 10 Hz for example.

Is this next formula I made right?

My doubt is, what's the relation between Hz and rad/s, f and w?

## 1 Answer

The formula you made will work if what you are after is simply "the area under the the magnitude plot from $\omega_i$ to $\omega_f$."

In many cases you can think of Hz as meaning "rotations per second." In that case, it becomes more obvious that 1 rotation = 2$\pi$ radians. Since $f$ has units of Hz and $\omega$ has units of radians, the conversion is simply: $$1 \, \text{Hz} = 2 \pi \, \frac{\text{rad}}{\text{s}}$$ So evaluate your integration from $\frac{1}{2\pi}$ to $\frac{10}{2\pi}$ and you should have the result you are after.

• @nisplo how come I didn't think in converting the unit?? :P Thank you very much. :) – SamuelNLP Aug 2 '13 at 23:17