- #1
Salmone
- 101
- 13
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?
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?