XPost: rec.audio.pro, comp.dsp   
   From: spam@spam.com   
      
   On Sat, 20 Nov 2010 08:03:14 +0000 (UTC), spope33@speedymail.org   
   (Steve Pope) wrote:   
      
   >Al Clark   wrote:   
   >   
   >>0 dBFS is a digital specification that represents the maximum level that a   
   >>data converter can convert. For example 0x7FFFFF... or 0x800000.. assuming   
   >>twos complement.   
   >>   
   >>It follows that the level of all signals will be <= 0 dBFS   
   >>   
   >>It has nothing to do with the rms level at all.   
   >   
   >I woulda said that a 0 dBFS signal has the RMS level of a sine wave   
   >that just barely doesn't clip  a converter (or, a hardlimited channel;   
   >it does not need to be a converter).   
   >   
   >(This is an important concept, of sorts, in that is shows that   
   >an N bit converter has a full-scale-signal to quantization noise   
   >ratio of 6*N + 2 dB, not the 6*N + 5 dB that some texts claim.)   
   >   
   >One can debate these things.  Most outcomes of such debates are   
   >equivalent within a factor of two.   
   >   
   >Steve   
      
   Here's how the maths works.   
      
   Lets call the clipping point 0dB.   
   The biggest sine wave it can hold is -3dB RMS. (peaks just clip).   
   The lowest bit level is - 16 * 20log(2), or -96.3dB   
      
   Because the converter is perfect, the noise is TPD, which has an RMS   
   value 4.8dB below the 1 bit peak. So the noise level is -101.1dB   
      
   So the dynamic range is 101.1dB -3dB +4.8 or 98.1dB. That is the range   
   from a just-clipping sine wave, to a signal equal in RMS amplitude to   
   the noise.   
      
   d   
      
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