Single bit ADC question

Somebody asked me this question and I was unsure of the answer.
It is well known that if you quadruple the sampling rate that you
reduce the quentisation noise by 6dB. Normally this means you can drop
off one bit.So if you have 12 bits you can make do with 11 bits by
sampling 4 times faster and maintain the same quantisation noise
level.
Taking this to its logical conclusion if we have 16 bits and we need
to use only one bit this means sampling at 4^15 = (approx) 10^9 times
as fast as you would normally. This seems kinda high?For instance if I
sample normally at 20kHz then I would need to sample at 20X10^12 Hz
for one bit.


Tom

"Tom" <aberdonian_2000@yahoo.com> wrote in message
news:e1b1658f.0310291242.39b8844a@posting.google.com...
> Somebody asked me this question and I was unsure of the answer.
> It is well known that if you quadruple the sampling rate that you
> reduce the quentisation noise by 6dB. Normally this means you can drop
> off one bit.So if you have 12 bits you can make do with 11 bits by
> sampling 4 times faster and maintain the same quantisation noise
> level.

I had thought it was one bit for each doubling, which is still pretty fast.


-- glen

aberdonian_2000@yahoo.com (Tom) wrote in message news:<e1b1658f.0310291242.39b8844a@posting.google.com>...
> Somebody asked me this question and I was unsure of the answer.
> It is well known that if you quadruple the sampling rate that you
> reduce the quentisation noise by 6dB. Normally this means you can drop
> off one bit.So if you have 12 bits you can make do with 11 bits by
> sampling 4 times faster and maintain the same quantisation noise
> level.
> Taking this to its logical conclusion if we have 16 bits and we need
> to use only one bit this means sampling at 4^15 = (approx) 10^9 times
> as fast as you would normally. This seems kinda high?For instance if I
> sample normally at 20kHz then I would need to sample at 20X10^12 Hz
> for one bit.
> 
> 
> Tom

Seem like Delta-Modulation to me(one bit ADC). Normally for
Delta-Modulation you will need to do oversampling. You will need a
very high sampling rate.

smallfriend

Tom wrote:

>Somebody asked me this question and I was unsure of the answer.
>It is well known that if you quadruple the sampling rate that you
>reduce the quentisation noise by 6dB. Normally this means you can drop
>off one bit.So if you have 12 bits you can make do with 11 bits by
>sampling 4 times faster and maintain the same quantisation noise
>level.
>Taking this to its logical conclusion if we have 16 bits and we need
>to use only one bit this means sampling at 4^15 = (approx) 10^9 times
>as fast as you would normally. This seems kinda high?For instance if I
>sample normally at 20kHz then I would need to sample at 20X10^12 Hz
>for one bit.
>
>
>Tom
>  
>
You can brute-force it this way. Practical applications use spectral 
shaping to move the quantization noise to higer-freq part of the 
spectrum, which is then eliminated by filtering. The result is a greater 
effective number of bits gained per doubling. ADI has nice tutorial 
material on the subject.

-- 
Kevin Hales
Catalpa Technology, Inc.
302 E. Davis St. Ste 211
Culpeper, VA 22701
540-727-8005

aberdonian_2000@yahoo.com (Tom) wrote in message news:<e1b1658f.0310291242.39b8844a@posting.google.com>...
> Somebody asked me this question and I was unsure of the answer.
> It is well known that if you quadruple the sampling rate that you
> reduce the quentisation noise by 6dB. Normally this means you can drop
> off one bit.So if you have 12 bits you can make do with 11 bits by
> sampling 4 times faster and maintain the same quantisation noise
> level.
> Taking this to its logical conclusion if we have 16 bits and we need
> to use only one bit this means sampling at 4^15 = (approx) 10^9 times
> as fast as you would normally. This seems kinda high?For instance if I
> sample normally at 20kHz then I would need to sample at 20X10^12 Hz
> for one bit.
> 
> 
> Tom

Hi Tom,

Have a look at the following application note :

http://www.maxim-ic.com/appnotes.cfm/appnote_number/1870

It gives a nice explanation on oversampling and the need for noise shaping.

Cheers,

Vijay.

On 29 Oct 2003 12:42:12 -0800, aberdonian_2000@yahoo.com (Tom) wrote:

>Somebody asked me this question and I was unsure of the answer.
>It is well known that if you quadruple the sampling rate that you
>reduce the quentisation noise by 6dB. Normally this means you can drop
>off one bit.So if you have 12 bits you can make do with 11 bits by
>sampling 4 times faster and maintain the same quantisation noise
>level.
>Taking this to its logical conclusion if we have 16 bits and we need
>to use only one bit this means sampling at 4^15 = (approx) 10^9 times
>as fast as you would normally. This seems kinda high?For instance if I
>sample normally at 20kHz then I would need to sample at 20X10^12 Hz
>for one bit.
>
>
>Tom

Hi Tom,
  just a quick comment.  If you quadruple the 
sampling rate, followed by lowpass filtering, 
you increase the signal to quantization noise ratio 
by roughly 6 dB.  Because we associate  6dB 
to be equivalent with having an extra bit in 
our binary time samples, we say that quadrupling 
the sample rate will gain you "one bit".

However, that "one bit" gain can only be had 
when filtering is performed.  And the filter 
must have coefficient word widths and multiplier/adder 
word widths wide enough to accommodate the 
increased signal to quant noise ratio.

See Ya',
[-Rick-]

I get uncomfortable with the assertation that by sampling 4 times as fast and 
then filtering and decimating it is possible to gain a reduction in 
quantization noise.  This assumes that the quantization noise is white and 
that filtering is noiseless.  Quantization is frequently modeled as white 
because a more accurate analysis is extremely difficult.  I'm not that 
convinced that the user will get that much of an improvement.

In article <3fa7a5a4.9956843@news.west.earthlink.net>, 
ricklyon@REMOVE.onemain.com (Rick Lyons) wrote:
>On 29 Oct 2003 12:42:12 -0800, aberdonian_2000@yahoo.com (Tom) wrote:
>
>>Somebody asked me this question and I was unsure of the answer.
>>It is well known that if you quadruple the sampling rate that you
>>reduce the quentisation noise by 6dB. Normally this means you can drop
>>off one bit.So if you have 12 bits you can make do with 11 bits by
>>sampling 4 times faster and maintain the same quantisation noise
>>level.
>>Taking this to its logical conclusion if we have 16 bits and we need
>>to use only one bit this means sampling at 4^15 = (approx) 10^9 times
>>as fast as you would normally. This seems kinda high?For instance if I
>>sample normally at 20kHz then I would need to sample at 20X10^12 Hz
>>for one bit.
>>
>>
>>Tom
>
>Hi Tom,
>  just a quick comment.  If you quadruple the 
>sampling rate, followed by lowpass filtering, 
>you increase the signal to quantization noise ratio 
>by roughly 6 dB.  Because we associate  6dB 
>to be equivalent with having an extra bit in 
>our binary time samples, we say that quadrupling 
>the sample rate will gain you "one bit".
>
>However, that "one bit" gain can only be had 
>when filtering is performed.  And the filter 
>must have coefficient word widths and multiplier/adder 
>word widths wide enough to accommodate the 
>increased signal to quant noise ratio.
>
>See Ya',
>[-Rick-]
>
>
>

nobody@nowhere.nothing wrote:

> I get uncomfortable with the assertation that by sampling 4 times as fast and 
> then filtering and decimating it is possible to gain a reduction in 
> quantization noise.  This assumes that the quantization noise is white and 
> that filtering is noiseless.  Quantization is frequently modeled as white 
> because a more accurate analysis is extremely difficult.  I'm not that 
> convinced that the user will get that much of an improvement.

It's actually pretty darn close, at least a delta sigma converter's
performance is, and there are even more things to go wrong in its
operation than a simple oversampling converter. And if you dither,
the quantization noise is indeed white. Yes, this stuff really works.
-- 
%  Randy Yates                  % "...the answer lies within your soul
%% Fuquay-Varina, NC            %       'cause no one knows which side
%%% 919-577-9882                %                   the coin will fall."
%%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

Randy Yates wrote:

> nobody@nowhere.nothing wrote:
>
> > I get uncomfortable with the assertation that by sampling 4 times as fast and
> > then filtering and decimating it is possible to gain a reduction in
> > quantization noise.  This assumes that the quantization noise is white and
> > that filtering is noiseless.  Quantization is frequently modeled as white
> > because a more accurate analysis is extremely difficult.  I'm not that
> > convinced that the user will get that much of an improvement.
>
> It's actually pretty darn close, at least a delta sigma converter's
> performance is, and there are even more things to go wrong in its
> operation than a simple oversampling converter. And if you dither,
> the quantization noise is indeed white. Yes, this stuff really works.
> --
> %  Randy Yates                  % "...the answer lies within your soul
> %% Fuquay-Varina, NC            %       'cause no one knows which side
> %%% 919-577-9882                %                   the coin will fall."
> %%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
> http://home.earthlink.net/~yatescr

It is white but I think it has a uniform distribution and not Guassian.

Tom

Tom wrote:

> 
> Randy Yates wrote:
> 
> 
>>nobody@nowhere.nothing wrote:
>>
>>
>>>I get uncomfortable with the assertation that by sampling 4 times as fast and
>>>then filtering and decimating it is possible to gain a reduction in
>>>quantization noise.  This assumes that the quantization noise is white and
>>>that filtering is noiseless.  Quantization is frequently modeled as white
>>>because a more accurate analysis is extremely difficult.  I'm not that
>>>convinced that the user will get that much of an improvement.
>>
>>It's actually pretty darn close, at least a delta sigma converter's
>>performance is, and there are even more things to go wrong in its
>>operation than a simple oversampling converter. And if you dither,
>>the quantization noise is indeed white. Yes, this stuff really works.
>>--
>>%  Randy Yates                  % "...the answer lies within your soul
>>%% Fuquay-Varina, NC            %       'cause no one knows which side
>>%%% 919-577-9882                %                   the coin will fall."
>>%%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
>>http://home.earthlink.net/~yatescr
> 
> 
> It is white but I think it has a uniform distribution and not Guassian.
> 
> Tom

Hi Tom,

Its distribution may be of academic interest, but in relation to this
problem it's irrelevent. As long as the spectrum is white, each doubling
of the sample rate yields pretty close to a 3 dB improvement in SNR.
-- 
%  Randy Yates                  % "...the answer lies within your soul
%% Fuquay-Varina, NC            %       'cause no one knows which side
%%% 919-577-9882                %                   the coin will fall."
%%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr