# How to select ADC resolution, considering input signal SNR and digital signal processing?

What I knew: The ADC resolution selection depends on the ADC inherent noise and input signal SNR.

Our application: Very high precision measurement of signals ranging 1kHz to 10kHz. We want to get as accurate result as possible, even 24-bit result.

The above statement, however, does not take digital signal processing after ADC sampling into consideration.

Since DSP techniques such as FIR, FFT and etc. may reduce the noises greatly, is it possible that increasing ADC resolution may also improve the measurement result when taking DSP techniques into consideration?

• One thing you didn't mention is the frequency of the signals you are trying to measure. This will be a key factor in determining what type of ADC you are going to use. – Nick Aug 18 '14 at 19:15
• @Nick , the frequency measured will be 1kHz --10kHz. And my main concern is "whether DSP matters when considering adc resolution.." Thanks for pointing that out, I will update the post. – richieqianle Aug 20 '14 at 9:22
• Resolution and sampling rate are interdependent - so if you were trying to characterize higher frequency signals at a high resolution everything else in your system would have to be clocked pretty fast. – Nick Aug 20 '14 at 13:52
• You are in a sweet spot for product availability because you're in the audible frequency range - there will be no shortage of 24bit ΣΔ ADCs. As I said in another comment - one issue you may face is the thermal/self-noise of your sensor. I've worked on projects where the sensor's noise floor was the limiting factor. That is probably something you should try to characterize before putting a lot of effort into the rest of the system. If your sensor doesn't have the dynamic range you need then it doesn't really matter how good the rest of your measurement hardware is. – Nick Aug 20 '14 at 14:15
• Another consideration: If you can use A LOT of sensors and synchronously sample the ADCs the uncorrelated noise will drop out when combine/average these signals. That is what we did in the aforementioned system I worked on (we had several hundred channels of audio), and that is also done commonly in the field of medical imaging: ncbi.nlm.nih.gov/pmc/articles/PMC2253211 – Nick Aug 20 '14 at 14:55

A general rule of thumb is that is you want something to not contribute to your noise budget, that it must be at least a factor of 10 higher SNR than the dominant noise source in your signal chain. As an example, if you have a signal source that is at 300 :1 SNR, run your ADC at 3000:1 and for all intents and purposes you can ignore the ADC.

The only way to do this properly is to do a noise analysis.

Post processing (via in DSP for example) has the potential to extract out salient features from above the noise but you have to be careful. You have to have sufficient bit depth so you don't introduce rounding/truncation errors. You have to ensure that you are conserving the nature of the noise (gaussian/poisson pdf) or else the noise floor may rise in an unpredictable way and may not be amenable to DSP techniques. These sorts of steps (matched filters etc.) typically at best can improve the SNR by factors of $\sqrt{N}$ and often the processing cost (# of operations) often follows $N^2$ so these sorts of steps often become rapidly very expensive. But agains a proper analysis will show this.

I would caution you against assuming that a DSP technique will automatically reduce your noise. It is very important that you lot at your noise sources via histogram analysis to ensure that the PDF (Probability Density Function) is amenable to processing. I.e. it appears well behaved, Gaussian or Poisson, is not multivariate and is stationary

• Thanks for your reply. Are you suggesting treating ADC resolution as quantization noises? Also the rounding/truncation errors are quantization noises I think, is that correct? Could you please introduce some good materials on Noise Analysis? I appreciate you pointing out that the DSP depends on noise nature, which I lack knowledge on..Also, by PDF you are talking about time-domain; isnt it correct to say that all noises can be filtered in frequency domain, how to relate them? – richieqianle Aug 20 '14 at 9:55
• ADC's do have quantization noise, resolution is related but something different. The N referenced is # of samples not bit depth. Time and frequency domain actions are inherently coupled and NO not all noise is amenable to being changed, one can easily introduce artifacts. – placeholder Aug 20 '14 at 14:08

• Thanks for your reply. Our application is very high precision measurement, as high as possible. May main question is "What is the influence of DSP(after adc sampling) on ADC resolution selection". – richieqianle Aug 16 '14 at 5:59
• @richieqianle - what I take Kyle to be saying/implying remains true after your comment - there are methods that can much improve resolvability of a small signal in a ton of noise but we don't know your specific application and therefore cannot know if any or some of these techniques apply. – Andy aka Aug 16 '14 at 9:14
• All a DSP does is preform mathematical calculations based on the information it gets from the ADC. Like Andy just stated, it still depends on your direct application. However, your going to need a high resolution ADC to get a high precision reading; typicaly. The noise that you might get depending on what your sampling must be eliminated as much as possible before the ADC. The DSP might be able to clean it up, but I don't like depending on them for that. – Kyle Aug 16 '14 at 19:29
• Having an ADC that has better resolution than the external signal noise is a waste of money.
• Having an ADC that has poor resolution and hence high inherent SNR can be countered by increasing the sampling rate of your process and implementing software recovery of the signal through filtering.
• If your signal bandwidth is known then a lot more can be done in algorithms to improve SNR by excluding noise - this is basically what an FFT does and software radio.

As we don't know much about your application it seems pointless pouring out detail that doesn't apply.

• I understand that external signal SNR decides the ADC precision when no DSP techniques are concerned..For the first point, do you mean that higher resolution will not help("better resolution than the external signal noise"), even if taking DSP techniques into consideration? – richieqianle Aug 16 '14 at 11:59

To get 24 bit precision you probably want a ΣΔ-ADC (Sigma-Delta ADC). Which is a special kind of 1-bit ADC (with noise-shaping) followed by filtering of the digital values.

The advantage of the ΣΔ-ADC is that with just one bit the quantization can't be nonlinear.

• This doesn't answer the question and additionally the modulator in a Sigma/Delta is non-linear like any thresholding operation. What is key is that that the DNL is monotonic and uniform in step, ie. it is uniformly non-linear. – placeholder Aug 17 '14 at 14:08
• Also, a 24 bit ΣΔ doesn't grantee 24 bits of resolution. You have N number of 'effective bits' which will depended on the noise floor of your system. I just want to throw this out there as a precaution - it is easy to think of this in the same way as a successive approximation ADC, but its a little different. – Nick Aug 18 '14 at 19:06
• Also - you can noise shape the quantization noise of the ADC out, but you shape other noise sources - like the thermal noise of your sensor. I've worked on systems with 24bit ADCs in the past and the limit of the system wasn't the ADC - it was the piezoelectric sensors. – Nick Aug 18 '14 at 19:20