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**hill0093****Member**- Registered: 2013-07-24
- Posts: 2

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) = ?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,861

hi hill0093

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

http://www.sosmath.com/trig/prodform/prodform.html

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.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**hill0093****Member**- Registered: 2013-07-24
- Posts: 2

Thanks Bob.

That's what I suspected.

I'll just plot graphically what I want to see.

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