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

# Multiple ADCs and aliasing

Started by ●February 23, 2018

Reply by ●February 23, 20182018-02-23

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, PiotrYou 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

Reply by ●February 23, 20182018-02-23

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

Reply by ●February 23, 20182018-02-23

benjamin.couillard@gmail.com wrote:> Check out this article from Analog Devices > > http://www.analog.com/en/analog-dialogue/articles/interleaving-adcs.htmlThanks 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

Reply by ●February 23, 20182018-02-23

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

Reply by ●February 23, 20182018-02-23

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.

Reply by ●February 24, 20182018-02-24

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. > > > MarcelIf 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

Reply by ●February 24, 20182018-02-24

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

Reply by ●February 24, 20182018-02-24

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, PiotrHi 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

Reply by ●February 25, 20182018-02-25

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