What is the Fourier transform of a beat? For example, I want to calculate the Fourier transform of the function $$f(t)=\cos((\omega_p+\omega_v) t)+\cos((\omega_p-\omega_v)t),$$ where $\omega_p+\omega_v=\Omega,\space\omega_p-\omega_v=\omega$ and $\Omega\simeq\omega.$
I think it is equal to $\frac{1}{2}(\delta(\omega_p+\omega_v-\omega)+\delta(\omega_p-\omega_v-\omega)+\delta(\omega_v-\omega_p-\omega)+\delta(-\omega_p-\omega_v-\omega))$, is it right?