Matt Bonner <mbonner@SUNADA.COM> wrote:

> Craig Webb wrote:
>
> > Thanks for the help. I'm running at about 2000 samps/sec (though I'd like to
> > run 8 channels!). We'll see how it goes. Some good suggestions though. How
> > many bytes would you use to keep good resolution at 13 bits? The person I'm
> > working with who has already written some LPF code said we need four byte to
> > keep precision. This seems a bit high to me.
> >
...
> First, you have to know the "noise-free" counts of your system.  This is
> typically your full scale signal divided by 6 times the rms noise - you
> find the rms noise by calculating the standard deviation of a sample set
> (I use a minimum of 1000 sample points).  Of course, this is only valid
> if your noise is Gaussian - plot your sample set to see.  Where did that
> "abritrary" value of 6 times come in?  If your data plot indicates that
> your noise is Gaussian, one standard deviation is equivalent to the rms
> noise.  Almost all of the data points will fall within +/-3.3 standard
> deviations - use a factor of 6 (close enough to 6.6) to estimate the
> peak-to-peak noise relationship to the rms noise.
>
> NOW, you can use averaging to improve system resolution.  BTW, thermal
> noise is typically the only true Gaussian noise that you're going to
> find.

True, but there is another problem as well. The numerical computation
in a digital filter is often ill-conditioned, and intermediate results
need to be stored with higher precision. How much depends on the
particular filter formula used, but according to my experience, a
doubling is not uncommon. 2 * 13 bits = 26, which is 3 bytes, plus
half a nibble.  I would say Craig's colleague's recommendation is very
reasonable.

Martin Nilsson                           http://www.sics.se/~mn/
Swedish Institute of Computer Science    E-mail: mn@sics.se
Box 1263, SE-164 29 Kista                Fax: +46-8-751-7230
Sweden                                   Tel: +46-8-752-1574