XPost: rec.audio.pro, comp.dsp   
   From: dpierce@cartchunk.org   
      
   glen herrmannsfeldt wrote:   
   > In comp.dsp davew  wrote:   
   >>We don't tend to use rms or mean whatever   
   >>when talking about audio levels though, we just say "level" and that   
   >>seems to be good enough.  It's understood that when you reach 0dBFS   
   >>you're in trouble shortly thereafter   
   >   
   > In EE, RMS can mean different things.   
      
   Not in any "EE" I ever encountered. It means one thing:   
      
       sqrt(sum(X1^2 + X2^2 ... +Xn^2) / n)   
      
   Now, what's partly at the root of this discussion is that   
   if we were to scale our system such that we called   
      
       max(abs(X1, X1 ...Xn))   
      
   "full scale," what is the ratio of the RMS value of that   
   set to the full scale value of that set.   
      
   And the answer is VERY definite: it depends upon the exact   
   content of the set. If all the values are the same, then   
   the ratio is 1, or 0 dB. Not a terribly useful signal, but   
   a valid one nonetheless.   
      
   If all the values were 0 and one was some non-zero value,   
   the ratio is is infinite.   
      
   If the values were the set defined by:   
      
       Xn = A sin(kn)   
      
   then the ratio of FS to RMS is 1/0.707. And for a square   
   wave, the ratio 1.   
      
   Ha, funny how the FS-to-RMS value of a square wave is the   
   same as for a DC voltage. The must sound the same! :-)   
      
   But, regardless, there aren't any "different versions" of   
   RMS, just the one:   
      
       sqrt(sum(X1^2 + X2^2 ... +Xn^2) / n)   
      
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