Aliasing in ADCs: Not all signals are what they appear to be

RE: Aliasing in ADCs: Not all signals are what they appear to be

Ryan Andrews — Tue, 27 Sep 2016 17:21:21 GMT

Hi Hari,

Even for DC inputs, the goal of an antialiasing filter remains the same - limit the bandwidth of the signal chain by attenuating out-of-band signals without interfering with the frequencies of interest. Just because you are measuring DC content, however, doesn't mean you need to set an ultra-low filter cutoff, nor should you for a couple reasons:

1. Real-world RC filters begin rolling off very early, so it is generally recommended to keep the -3dB point at least a couple decades beyond your frequencies of interest. Also, the lower your make the filter cutoff, the larger the passive components typically become, which can introduce other types of errors in your measurement (i.e. large resistors introduce offset in the presence of input bias currents).

2. The digital filter in delta-sigma ADCs can help a lot with attenuating out-of-band noise. The output data rate can often be chosen such that the digital filter -3dB cutoff is very low (< 1Hz in some devices like our ADS1262). The response of these filters begins at 0dB and repeats at multiples of the modulator frequency (fMOD). The primary goal for your antialiasing filters then becomes to attenuate the noise around n*fMOD only; otherwise, noise in that range will fold back into your passband. This means your RC filter cutoff can be set further in frequency and the response can be more gradual.

I have a couple more blogs on this very topic; check them out if you're interested!

Regards,

Ryan

RE: Aliasing in ADCs: Not all signals are what they appear to be

Hari Thazhe Oyyoth — Tue, 20 Sep 2016 08:58:44 GMT

Hi Ryan,

Could you please tell me how anti aliasing filters behave to a DC input. How to select filter cut off frequency for DC inputs.

RE: Aliasing in ADCs: Not all signals are what they appear to be

Steve MacLeod — Thu, 15 Oct 2015 14:29:38 GMT

It's easy to see pictorially that sampling a signal at twice its rate will not yield its frequency. Draw a sine wave and mark samples every 180 degrees. It doesn't matter where you start, from symmetry, all the points will add to zero.

RE: Aliasing in ADCs: Not all signals are what they appear to be

Ryan Andrews — Tue, 06 Oct 2015 15:41:09 GMT

Hi Ken,

I agree, there are inconsistencies amongst a number of definitions out there as to whether the '=' is included or not. In the end, I hope it's clear that sampling at exactly 2*fmax is generally insufficient and therefore impractical in most ADC applications.

Thank you both for your comments!

RE: Aliasing in ADCs: Not all signals are what they appear to be

Ken Dillinger — Mon, 05 Oct 2015 17:59:16 GMT

I agree with Donald.

The problem I have seen is that there are inconsistencies between text books. Some will state that the Nyquist Rate is 2*fmax >= fs while others will state 2*fmax > fs. I have always been taught that the sampling rate must be more than twice the maximum frequency of interest. Oppenheim & Wilsky, Signals & Systems states this (see page 519).

In fact, Tim Wescott from Wescott Design Services posted a paper on this very subject some time ago, "Sampling: What Nyquist Didn't Say And What To Do About It."

RE: Aliasing in ADCs: Not all signals are what they appear to be

Ryan Andrews — Mon, 21 Sep 2015 20:25:30 GMT

Hi Donald,

Thanks for your comment. By definition, the Nyquist theorem calls for a sampling rate of at least twice the input frequency. However, we know that in practice, a sampling rate of exactly 2x is not sufficient to represent it correctly in the digital domain. For all you know, you may be sampling the signal at the zero-crossing each time, resulting in a DC output. If instead your samples fell in line with the signal's min and max (or any other part of the signal for that matter), you would still get information about the signal's frequency, but not enough information to determine it's amplitude or shape with any certainty.

Regards,

Ryan

RE: Aliasing in ADCs: Not all signals are what they appear to be

Donald Reay — Thu, 10 Sep 2015 14:55:22 GMT

I think you mis-state the Nyquist theorem.

According to the Nyquist theorem, an ADC must sample the input signal more than (not 'at least') twice as fast as its highest-frequency component.

You effectively concede this later on.

At exactly 12SPS, the 6-Hz input will still fold back to DC and add an offset to the measurement, so sampling just a little faster ensures that your signals of interest do not alias at all.