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#1 2013-07-24 07:42:42

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) = ?


#2 2013-07-25 06:24:15

bob bundy
Registered: 2010-06-20
Posts: 7,579

Re: trignometry

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   sad so I'll jump in with what little I know dizzy .  Maybe that will spur someone else to tell me I'm wrong and then we'll get somewhere.  smile

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.


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei


#3 2013-07-28 03:07:46

Registered: 2013-07-24
Posts: 2

Re: trignometry

Thanks Bob.
That's what I suspected.
I'll just plot graphically what I want to see.


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