Absolute and signed beat envelopes
= Absolute and signed beat envelopes
For $x_2=(a/2)[\cos\omega_1t-\cos\omega_2t]$, the slowly varying signed factor is $a\sin[(\omega_2-\omega_1)t/2]$. The absolute amplitude envelope repeats in $2\pi/|\omega_2-\omega_1|$, half the period of that signed factor.