Butterworth

On 10/25/13 1:56 AM, niarn wrote:
>>
>> i like to define it as the dB of SNR plus the dB of headroom.
>
> That makes sense to me because the headroom could just as well be used to
> gain up the input and thus increase SNR.

to a point.  that's why i think you need to specify a decent mid-level 
output (like 6 dB below the rails is what i would suggest).  but if you 
crank it up too high, you'll lose *both* headroom and SNR.

> One practical issue I can think of
> with this approach is that if some non-stationary input is used for the
> measurement it may be difficult to find or track what the headroom should
> be. I assume you mean the margin up to fullscale as being the headroom.

yes.  my nomenclature for "fullscale" is "rails".

> What type of input would you use for your SNR measurement? sweep,
> sinusoidal, noise?

whatever.  that's a spec.  but to compare apples to apples, you need to 
account for that 1.76 dB you get from a sine wave compared to a signal 
that has uniform p.d.f. up to its maximum value.  the margin between the 
maximum and the rail (or "ceiling" or "fullscale") is, by definition i 
think, the headroom.

i like that uniform distribution (which you get with a triangle or 
sawtooth wave without DC) for the test signal because then there is no 
1.76 dB factor (or any other) and the p.d.f. of the S (in S/N) is the 
same as the p.d.f. of the N (at least undithered N).  and then you get a 
very clean formula for DynamicRange = (6.02 dB)*(word width in bits).

if you use a sinusoid, you would have to add 1.76 dB.  and if you use 
maximum-length sequences for the driving signal and you jacked that up 
to the rails, i think you get another 3.01 dB S/N more than the sine. 
but i would never recommend driving a system to the rails with an MLS. 
nor even a sine wave.  just seems like asking for trouble.  you may get 
distortion components in the D/A or something.

>
>> these two
>> quantities add roughly to a constant, at least for mid-level output.
>
> Do you mean that for mid-level output there is very little risk of internal
> wraparound or saturation that could impact the measurement?

yeah, like 6 dB below the rails.  but the SNR+HR should still be about 
the same if you're 12 dB below the rails (6 dB less SNR and 6 dB more 
HR).  but you wouldn't want to make this measurement 6 or 12 dB above 
the LSB.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."