XPost: rec.music.gdead, sci.electronics.design   
   From: dpierce@cartchunk.org   
      
   SoothSayer wrote:   
   > On Fri, 04 Mar 2011 08:55:23 +0100, Jeroen Belleman   
   >  wrote:   
   >   
   >   
   >>SoothSayer wrote:   
   >>   
   >>>[...]   You have to MODULATE the AMPLITUDE of a   
   >>>"carrier" with the intended "signal"..   
   >>>   
   >>>  Simply seeing something that appears to be "enveloped" does not mean   
   >>>that it is amplitude modulated. Linear summation does not get you there.   
   >>   
   >>Time for a trigonometry refresher course:   
   >   
   >  Are you sure?  Could it be semantics?   
      
   No, something more fundamental than that: bad   
   assumpti8ons.   
      
   >>Modulation is multiplication of two signals, e.g., for sine waves   
   >>cos A * cos B.   
   >   
   >   Funny, I thought modulation was using one signal to control the   
   > amplitude of another signal.   
   >   
   > Multiplication?   
      
   That's what modulation is.   
      
   >>A basic trigonometric identity tells us this is identical to:   
   >>0.5 cos(A+B) - 0.5 cos(A-B), which is a simple linear sum of   
   >>sine waves.   
   >   
   >   Is it identical?   
      
   Yes, identical.   
      
   >Are you saying "sum" or "multiply"?  They are   
   > different words.  You should choose one.   
      
   No, because you have two operations through   
   different paths give the IDENTICAL result.   
      
   >>In conclusion, your assertion that linear summation can't   
   >>get you a modulated waveform is wrong.   
   >>   
   >   
   > The 'waveform' is not what is required to be modulated   
    > to qualify as AM.  The amplitude of a carrier has to be   
    > modulated by the second signal.   
      
   That's true if you choose that path. The result of modulation   
   of a carrier by a signal IS the multiplecation of the carrier   
   by the signal.   
      
   And when you do that multiplication using, in a simple example,   
   a sine wave carrier of frequency f1 and a modulating signal   
   of frequency f2, the result is THREE components, f1, f1-f2   
   and f1+f2.   
      
   AND, if you choose a different path, taking three sine   
   waves of frequency f1, f1-f2 and f1+f2, each generated   
   INDEPENDENTLY and perform a linear sum, and that means   
   ADD, you will get the IDENTICAL modulated waveform.   
      
   >  Simple summation of the two signals is a summated pair of sine waves.   
      
   No, in the example I gave earlier, I DID NOT say the summation of   
   TWO sine waves, I said the sumation of THREE sine waves.   
      
   That's VERY different than what you are claiming.   
      
   > Shows up a little different on the scope. Besides, you said multiply, not   
   > sum.  So, two tens gets you a hundred?   
      
   Yes, if you, in fact, do the wrong thing, you get the wrong results.   
      
   > Modulating the amplitude of one sine wave with the other is a different   
   > injection method.  Two tens will get you twenty.   
      
   Instead, do the righ thing: do NOT sum 100 Hz and 1000 Hz to get   
   the equivalent of a 1000 Hz carrier modulated by a 100 Hz signal.   
   If that's what you are doing, you're doing the worng thing.   
      
   Instead, sum (add) 900 Hz, 1000 Hz and 1100 Hz of the right   
   phases and amplitudes, and it WILL BE IDENTICAL to a 1000Hz   
   carrier modulated (multiplied) by a 100 Hz signal.   
      
   If you disagree, talk to Arnie: he borrowed my shovel   
   and you're more than welcome to dig up Mr. Fourier and   
   tell him how wrong he is.   
      
   Let us know how it works out for you.   
      
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