Multiple ADCs and aliasing

I have two 1MHz ADCs and would like to interleave them
by a half of the sampling cycle in order to get a single
ADC with effective sampling frequency of 2MHz (I want to
oversample the signal by as much as possible). But the
aliasing properties of the data stream will be as if the
signal was sampled at 1MHz because the ADCs are independent
blocks and don't influence each other, right?

	Best regards, Piotr

On 2/23/2018 3:41 AM, Piotr Wyderski wrote:
> I have two 1MHz ADCs and would like to interleave them
> by a half of the sampling cycle in order to get a single
> ADC with effective sampling frequency of 2MHz (I want to
> oversample the signal by as much as possible). But the
> aliasing properties of the data stream will be as if the
> signal was sampled at 1MHz because the ADCs are independent
> blocks and don't influence each other, right?
> 
>      Best regards, Piotr

You would need to trigger the two ADCs on the halves of the sampling 
cycle.  I think you implied that. Because the ADCs are triggered with a 
fixed phase it's not correct to say they are independent blocks.

Depending on the circuit details, you may need sample and hold circuits 
on each ADC input.

Try a thought experiment. Use your ADC system to read a 1 MHz square 
wave that is in phase with your sampling signal.  ADC #1 always sees 1V, 
and ADC #2 always sees 0V.

-- 
Best wishes,
--Phil
pomartel At Comcast(ignore_this) dot net

Le vendredi 23 f=C3=A9vrier 2018 03:41:07 UTC-5, Piotr Wyderski a =C3=A9cri=
t=C2=A0:
> I have two 1MHz ADCs and would like to interleave them
> by a half of the sampling cycle in order to get a single
> ADC with effective sampling frequency of 2MHz (I want to
> oversample the signal by as much as possible). But the
> aliasing properties of the data stream will be as if the
> signal was sampled at 1MHz because the ADCs are independent
> blocks and don't influence each other, right?
>=20
> 	Best regards, Piotr



Check out this article from Analog Devices

http://www.analog.com/en/analog-dialogue/articles/interleaving-adcs.html

benjamin.couillard@gmail.com wrote:

> Check out this article from Analog Devices
> 
> http://www.analog.com/en/analog-dialogue/articles/interleaving-adcs.html

Thanks Benjamin and Phil, very informative! The issue turns out to be
much more complex than I thought, but the graphs are also very promising 
-- the spurious spikes are exactly in the places where the signal isn't.

	Best regards, Piotr

On 23.02.18 09.41, Piotr Wyderski wrote:
> I have two 1MHz ADCs and would like to interleave them
> by a half of the sampling cycle in order to get a single
> ADC with effective sampling frequency of 2MHz (I want to
> oversample the signal by as much as possible). But the
> aliasing properties of the data stream will be as if the
> signal was sampled at 1MHz because the ADCs are independent
> blocks and don't influence each other, right?

If your ADC act as sample-and-hold then you have all properties of a 2 
MHz ADC - assuming that they really sample alternatingly at 2MHz, of course.

If your ADC have some analog bandwidth limitations, e.g. by averaging, 
then this bandwidth will be unchanged by the second ADC.


Marcel

Marcel Mueller  <news.5.maazl@spamgourmet.org> wrote:

>If your ADC act as sample-and-hold then you have all properties of a 2 
>MHz ADC - assuming that they really sample alternatingly at 2MHz, of course.

Yes, you really do want to simulate the effect of the possible
sample time offset.  I seem to recall there are weird artifacts,
the effect of which is dependent on application.

S.

On 2/23/2018 5:14 PM, Marcel Mueller wrote:
> On 23.02.18 09.41, Piotr Wyderski wrote:
>> I have two 1MHz ADCs and would like to interleave them
>> by a half of the sampling cycle in order to get a single
>> ADC with effective sampling frequency of 2MHz (I want to
>> oversample the signal by as much as possible). But the
>> aliasing properties of the data stream will be as if the
>> signal was sampled at 1MHz because the ADCs are independent
>> blocks and don't influence each other, right?
> 
> If your ADC act as sample-and-hold then you have all properties of a 2 
> MHz ADC - assuming that they really sample alternatingly at 2MHz, of 
> course.
> 
> If your ADC have some analog bandwidth limitations, e.g. by averaging, 
> then this bandwidth will be unchanged by the second ADC.
> 
> 
> Marcel
If there's a S&H before the ADC (whether part of the ADC or a separate 
circuit), you can treat the ADC as a black box independent of how it 
works inside.  The analog bandwidth was stated to be 1 MHz.

-- 
Best wishes,
--Phil
pomartel At Comcast(ignore_this) dot net

On 2/23/2018 1:50 PM, benjamin.couillard@gmail.com wrote:
> Le vendredi 23 février 2018 03:41:07 UTC-5, Piotr Wyderski a écrit :
>> I have two 1MHz ADCs and would like to interleave them
>> by a half of the sampling cycle in order to get a single
>> ADC with effective sampling frequency of 2MHz (I want to
>> oversample the signal by as much as possible). But the
>> aliasing properties of the data stream will be as if the
>> signal was sampled at 1MHz because the ADCs are independent
>> blocks and don't influence each other, right?
>>
>> 	Best regards, Piotr
> 
> 
> 
> Check out this article from Analog Devices
> 
> http://www.analog.com/en/analog-dialogue/articles/interleaving-adcs.html
> 
Excellent article.  Thanks.

-- 
Best wishes,
--Phil
pomartel At Comcast(ignore_this) dot net

Piotr Wyderski <peter.pan@neverland.mil> writes:

> I have two 1MHz ADCs and would like to interleave them
> by a half of the sampling cycle in order to get a single
> ADC with effective sampling frequency of 2MHz (I want to
> oversample the signal by as much as possible). But the
> aliasing properties of the data stream will be as if the
> signal was sampled at 1MHz because the ADCs are independent
> blocks and don't influence each other, right?
>
> 	Best regards, Piotr

Hi Piotr,

Great question! I don't think anyone has really answered it. Here is my
shot at it. Note that my answer is in the theoretical realm and I do not
consider practical problems such as gain mismatch, DC offset mismatch,
etc.

You are right. If the input signal to either of the ADCs has a bandwidth
greater than Fs / 2, where Fs = 1 MHz, then you will have aliasing and
that will be bad/unrecoverable.

However, theoretically you can do this like follows:

  1. Split the input signal spectrum into two components: 0 <= S1(w) <
  Fs / 2, and Fs / 2 <= S2(w) < Fs. ("w" here means Greek omega, i.e.,
  radian frequency, w = 2 * pi * f.)

  2. Feed S1 into ADC1 and S2 into ADC2.

  Since each ADC's input is bandlimited to Fs/2, you will get no
  aliasing.

  3. Stitch the output of each ADC back together as follows:

     a. Interpolate ADC1 by two to Fs. Call this I1(w).

     b. Interpolate ADC2 by two to Fs. Call this I2(w).

     c. Mix I2 up by Fs/2. Call this IM2.

     d. Form the final output signal Y = I1 + IM2.

I hope this is clear. There are undoubtedly other ways to do this, but
this seems the easiest to conceive of.
-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com

Randy Yates <yates@digitalsignallabs.com> writes:

> Piotr Wyderski <peter.pan@neverland.mil> writes:
>
>> I have two 1MHz ADCs and would like to interleave them
>> by a half of the sampling cycle in order to get a single
>> ADC with effective sampling frequency of 2MHz (I want to
>> oversample the signal by as much as possible). But the
>> aliasing properties of the data stream will be as if the
>> signal was sampled at 1MHz because the ADCs are independent
>> blocks and don't influence each other, right?
>>
>> 	Best regards, Piotr
>
> Hi Piotr,
>
> Great question! I don't think anyone has really answered it. Here is my
> shot at it. Note that my answer is in the theoretical realm and I do not
> consider practical problems such as gain mismatch, DC offset mismatch,
> etc.
>
> You are right. If the input signal to either of the ADCs has a bandwidth
> greater than Fs / 2, where Fs = 1 MHz, then you will have aliasing and
> that will be bad/unrecoverable.
>
> However, theoretically you can do this like follows:
>
>   1. Split the input signal spectrum into two components: 0 <= S1(w) <
>   Fs / 2, and Fs / 2 <= S2(w) < Fs. ("w" here means Greek omega, i.e.,
>   radian frequency, w = 2 * pi * f.)
>
>   2. Feed S1 into ADC1 and S2 into ADC2.
>
>   Since each ADC's input is bandlimited to Fs/2, you will get no
>   aliasing.
>
>   3. Stitch the output of each ADC back together as follows:
>
>      a. Interpolate ADC1 by two to Fs. Call this I1(w).
>
>      b. Interpolate ADC2 by two to Fs. Call this I2(w).
>
>      c. Mix I2 up by Fs/2. Call this IM2.
>
>      d. Form the final output signal Y = I1 + IM2.
>
> I hope this is clear. There are undoubtedly other ways to do this, but
> this seems the easiest to conceive of.

Piotr,

I should have thought of this when I first saw your post. I'm surprised
no one has mentioned it thus far.

Another method of getting 2x the bandwidth using 2 ADCs is to process
the input signal into two signals which are in quadrature, i(t) and
q(t), then form the output signal as y(t) = i(t) + j * q(t), i.e., the
output signal becomes complex. Again, each of i(t) and q(t) must be
limited to Fs / 2 to avoid aliasing as you said. However the final
signal will have 2x the bandwidth, -Fs / 2 <= Y(f) < +Fs / 2. That is,
the negative portion of the spectrum will carry information as well as
the positive portion.

If the input signal is from an IF or RF carrier, one method to generate
quadrature signal is to use quadrature downconversion or quadrature
mixing.

I'm not sure if staggering the ADCs by one-half the sample period is
equivalent to qaudrature sampling at baseband. I think so but it's not
clear to me right this momemnt.
-- 
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com