From common trigonometric formulas, I know that
A cos(2πF1t) + A cos(2πF2t) = 2A cos(2π[(F1-F2)/2]t) cos(2π[(F1+F2)/2]t)
where A is the amplitude of both original cosine functions of t, and F1 and F2 are their respective frequencies, the product demonstrates a modulation of the cosine of the average frequency.
Is there a similar product formula if the two original amplitudes are different, i.e..:
A1 cos(2πF1t) + A2 cos(2πF2t) = ?
Welcome to the forum.
I hung on hoping someone who knows the answer would post, but it doesn't look like they will so I'll jump in with what little I know . Maybe that will spur someone else to tell me I'm wrong and then we'll get somewhere.
The first result comes from this trig formula
So it works because the amplitudes are the same.
I'm fairly certain there's no formula when the amplitudes are different. There might be one when one amplitude is a simple factor of the other.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei