Warp wrote:

>   Basically you are saying that you can recreate a sine wave (which is one
> single frequency) with the sum of two sine waves (the two frequencies in
> the discrete frequency spectrum)? Not only that, but the two sine waves
> in question are adjacent to each other in the discrete frequency spectrum?
> 
>   I would be interested in seeing some simple math about this.

   sin x + sin y = 2 cos (x-y)/2 sin (x+y)/2

If we replace x and y with jt and kt, we have

   sin jt + sin kt = 2 cos t(j-k)/2 sin t(j+k)/2

If j and k are very close, (j-k)/2 would be nearly zero, so the cos term 
would be nearly unity. Then we would have just

   sin jt + sin kt = 2 sin t(j+k)/2

In other words, a sine wave who's frequency is the arithmetic mean of 
the frequences of the two waves being added. QED.

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