XPost: rec.music.gdead, sci.electronics.design   
   From: jeroen@nospam.please   
      
   John Fields 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:   
   >>   
   >> Modulation is multiplication of two signals, e.g., for sine waves   
   >> cos A * cos B.   
   >>   
   >> 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.   
   >>   
   >> In conclusion, your assertion that linear summation can't   
   >> get you a modulated waveform is wrong.   
   >>   
   >> Jeroen Belleman   
   >   
   > ---   
   > No, he's right:   
      
   I tell you, he's wrong. What you did is not what the above   
   formula said.   
      
   Substitute   
   V2 =  SINE(0 .5 10100 0 0 90)   
   and   
   V3 = SINE(0 .5 9900 0 0 -90)   
      
   and you'll see that the waveform from the adder matches that of   
   the modulator exactly. The spiel with the phase of the sources is   
   because LTspice generates sines rather than cosines, which is of   
   no importance to the argument.   
      
   I rest my case.   
      
   Jeroen Belleman   
      
   --- SoupGate-Win32 v1.05   
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