Multiplication of Sinusoids

To apply an envelope on a signal, the envelope is multiplied by the signal.

The results then suggest that adding two sinusoids close in frequency is the same as multiplying two sinusoids, in this case, one low-frequency.

This can be shown mathematically to be true!

Cosine Product formula,

$$\cos(a)\cos(b) = \frac{\cos(a+b) + \cos(a-b)}{2},$$

we can show that

$$x(t) = \cos(2\pi(220)t)\cos(2\pi(2)t)$$

$$= \frac{1}{2}\left[\cos(2\pi(222)t)+\cos(2\pi(218)t)\right].$$