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   XPost: rec.audio.pro, comp.dsp   
   From: spam@spam.com   
      
   On Fri, 26 Nov 2010 03:07:24 -0800 (PST), Chris Bore   
    wrote:   
      
   >On Nov 22, 3:36 pm, Dick Pierce  wrote:   
   >> Arny Krueger wrote:   
   >> > "Dick Pierce"  wrote in message   
   >> >>The term "instantaneous RMS value" is itself meaningless.   
   >>   
   >> > Right, because RMS has to be averaged over an interval.   
   >>   
   >> > Instantaneous peak values can be meaningful, but in the digital domain   
   they   
   >> > aren't really instantaneous. They correpond to a sample interval.   
   >>   
   >> Which Shannon and Nyquist would tell us is in a properly   
   >> implemented system, is indistiguishable from instantaneous.   
   >> It makes no difference if during that interval the signal   
   >> was continuously at some level or was a unit impulse at   
   >> that level or a bunch of noise that averaged out at that   
   >> same level.   
   >   
   >With two provisos:   
   >   
   >1) The peak value of the samples is not necessarily the peak value of   
   >the continuous waveform that was sampled. To estimate the peak value   
   >of the continuous waveform you would have to interpolate to some up-   
   >sampled rate capable of captruing all possible peak excursions, or   
   >convert through an appropriate reconstruction filter to an analog   
   >waveform whose peak you could then measure.   
   >   
   And of course this is exactly how it is done. In a high end DAC, the   
   reconstruction oversampler will implement an extra bit to properly   
   reconstruct inter-sample peaks. Of course this could, in theory at   
   least, be done without oversampling with a steep enough analogue   
   filter.  The inter-sample peaks would be reproduced properly. In   
   either case dBFS will refer to the maximum digital value sampled - the   
   analogue level that gave rise to it is immaterial.   
      
   >2) A waveform that can be sampled according to Shannon cannot contain   
   >an impulse, since it must be band limited, so the point about an   
   >impulse is moot   
   >   
      
   Impulses are not necessarily zero width. An impulse is pretty much   
   what you define it to be. Anything non-repetitive can be considered an   
   impulse. The Dirichlet conditions for FFT-ability cover this very   
   well.   
      
   d   
   >Chris   
   >==============================   
   >Chris Bore   
   >BORES Signal Processing   
   >www.bores.com   
   >   
   >>   
   >> --   
   >> +--------------------------------+   
   >> +         Dick Pierce            |   
   >> + Professional Audio Development |   
   >> +--------------------------------+   
      
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