beating by adding two signals

[pietpara]

I am relatively new to this topic so I have some trouble understanding the following problem.

I add two sine waves with a difference frequency and amplitude. The resulting signal shows a amplitude modulated signal at the beating frequency.

I am trying to sort of prove (mathematically) that this is equivalent to standard amplitude modulation such that I can also use standard demodulation techniques to obtain the signal of interest, namely the amplitude modulation signal.

However, I realise that, although this comes quite close to a standard amplitude modulated signal (as seen in Tutorial 9), it is not really the same.
The difference seems to be that I do not have a fixed carrier signal at a fixed frequency with two side bands.

My question is how I can see this problem as analogous to standard AM and how could such a signal be demodulated; i.e. how can I best obtain the amplitude modulation signal?

thanks
Pietpara

[cbee1]

Okay, This is my off the top opinion: Just as you can arrive at the number 12 by adding numbers such as 6 and 6 together,which is analogous to sinusoidal addition, when it comes time to find that number tweleve via the product of two numbers, you have a lot of options, such as 3 and 4, 2 and 6, etc. So, The thing is, if you have a composite wave, you have no way of knowing which specific set of frequencies, out of many would form that composite wave. You may break everything down and realise that you have 20 sets of numbers that could produce that composite wave via multiplication/amplitude modulation. Now, if you have devised some kind of statistical way to pin point the specific set that you are looking for out of the larger group, then what you are saying will work. Other than that, I don't really see a way. That is just my opinion of what it ultimately appears you're trying to do. I'm open to any criticism on my point.

[cbee1]

One small change.

The thing is, if you have a composite wave, you have no way of knowing which specific set of frequencies out of many would form that composite wave "via multiplication".

[idanman]

OK. The way this works is as follows:
cos((w1+w2)t)+cos((w1-w2)t)=2cos(w1t)cos(w2t)
If you are beating 1 and 2 hz signals it's equivalent to multiplying 1.5hz by 0.5 hz signals -- ie AM modulating a carrier of 1.5hz with 0.5hz.