# Amplitude Modulation Phenomona

by dmorr
Tags: amplitude, modulation, phenomona
 P: 4,663 The product of a small amplitude modulation on a carrier can be represented by $\left(1+A\cos\omega_1t \right)\cos\omega_2t$. This can be rewritten as $$\left(1+A\cos\omega_2t \right)\cos\omega_1t=\cos\omega_1t +A\cos\omega_2t\cos\omega_1t =\cos\omega_1t + \frac{A}{2} \cos\left(\omega_1-\omega_2 \right)t+\frac{A}{2} \cos\left(\omega_1+\omega_2 \right)t$$ So the tremulo modulation produces sum and difference sidebands at any amplitude modulation frequency. So not being able to hear the sidebands as new frequencies might be just due to sound perception (see http://en.wikipedia.org/wiki/Psychoacoustics.)