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## Main Question or Discussion Point

Okay: here's the question:

It's a well-known thing that when you add two sinusoids of equal amplitude and different frequency then you end up with a signal with the mean of the frequencies and a beat envelope. This just comes from the trig identity:

[tex]\cos(a) + \cos(b) = 2\cos(\frac{a+b}{2}) \cos(\frac{a-b}{2})[/tex]

Now... here's the tricky bit: what happens if the two signals have different amplitudes?

I can get some kind of intuitive feel for what would happen by considering the limit of one signal being much stronger than the other, but I'd really like to be able to find some formula, similar to the above, perhaps with a form similar to this:

[tex]A\cos(a) + B\cos(b) = (A+B)\cos(x)(1-z\cos(y))[/tex]

where x is the signal frequency, y is the beat frequency, and z is some number determining by how much the signal amplitude varies due to the beats.

Or perhaps this isn't possible? Anyhow: does anyone have any ideas?

It's a well-known thing that when you add two sinusoids of equal amplitude and different frequency then you end up with a signal with the mean of the frequencies and a beat envelope. This just comes from the trig identity:

[tex]\cos(a) + \cos(b) = 2\cos(\frac{a+b}{2}) \cos(\frac{a-b}{2})[/tex]

Now... here's the tricky bit: what happens if the two signals have different amplitudes?

I can get some kind of intuitive feel for what would happen by considering the limit of one signal being much stronger than the other, but I'd really like to be able to find some formula, similar to the above, perhaps with a form similar to this:

[tex]A\cos(a) + B\cos(b) = (A+B)\cos(x)(1-z\cos(y))[/tex]

where x is the signal frequency, y is the beat frequency, and z is some number determining by how much the signal amplitude varies due to the beats.

Or perhaps this isn't possible? Anyhow: does anyone have any ideas?