Re: Compensating DAC for low bit-resolution with high sample rate

On Thu, 15 Nov 2007 22:31:26 -0500, Randy Yates wrote:

Tim Wescott <tim@xxxxxxxxxxxxxxxx> writes:
[...]
At this point I'm really not sure what _you're_ driving at.

Consider the following thought experiment. We design an oversampling
system that uses a 10-bit DAC to run at 16*Fs, where Fs is the original
sample rate. Therefore we expect to get 12 bit performance at the
output.

However, our 10-bit DAC was a rip-off and essentially threw the 2 LSBs
completely away, i.e., it was really an 8-bit DAC.

Now that device would have a really lousy differential non-linearity,
but that doesn't completely negate the benefit of oversampling. In fact,
it doesn't negate it at all. What will happen is that the output will be
the equivalent of a 10-bit DAC, i.e., the oversampling still adds 2 bits
of resolution, but we lose 12 dB due to the quality (or lack thereof) of
the DAC.

THAT'S the type of effect I'm driving at, and THAT'S why I say I'm not
so sure you can just conclude that any distortion/nonlinearity in the
DAC is going to completely negate any gain afforded by oversampling, and
with a little more thought I think it might include noise-shaping as
well.

Am I wrong? Show me where.

I never concluded that. In fact, I advocate using noise shaping to gain
resolution when you need resolution but can throw accuracy out the window:
http://www.wescottdesign.com/articles/sigmadelta.html.

I was just trying to steer the OP away from thinking that a 12-bit DAC
with 16x oversampling (with or without noise shaping) is going to give
performance comparable to a 16-bit DAC -- it won't, unless it's an unusual
12-bit DAC.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
.

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