# What's the actual sampling rate of an ADC that is only enabled periodically?

Let's say I have and ADC that samples at $f_{adc}$ when enabled by a CPU. The CPU executes a loop in which the ADC is enabled for $T_{en\_adc}$ and the remaining time something else is done for $T_{other}$, so that $T_{loop}=T_{en\_adc} + T_{other}$. When the ADC is not enabled, samples are not stored anywhere, the ADC does nothing at all.

At what frequency I'm actually sampling the signal then? Is it still meaningful to talk about frequency and sampling rate?

(everything in second/hertz)

• If you don't sample at all your sample rate is 0 Hz. – arminb Nov 24 '17 at 13:14
• That really depends on what you are sampling. If it is something that does not change quickly (like temperature), Shannon-Nyquist does not apply. – StainlessSteelRat Nov 24 '17 at 13:14
• @StainlessSteelRat Of course it applies. "If it is something that does not change quickly (like audio), Shannon-Nyquist does not apply." - See what I did there? – pipe Nov 24 '17 at 13:27
• What the hell? The sampling theorem always apply, from 0 to $\infty$ bandwidth. – Vladimir Cravero Nov 24 '17 at 14:35
• @pipe Audio has an upper frequency, so Shannon-Nyquist applies. But a lot of real-world data is 0Hz (DC, temperature, pressure, etc.) and any sampling is generally over-sampling that is more dependent on application. You cannot answer this question without knowing the characteristics of the signal to be sampled. – StainlessSteelRat Nov 24 '17 at 18:11

That kind of sampling will lead to aliasing with something roughly like a sinc response if there is frequency component in the input above $\frac{1}{2(T_{en\_adc} + T_{other})}=\frac{f_{en\_adc}+f_{other}}{2}$. The shorter the bursts of samples in relation to the entire cycle, the closer it it will approach simply sampling at the lower frequency.

It depends on the characteristics of your signal, and what you're trying to do.

If during a time of $T_{en\_adc}$ you sample at $f_{adc}$, you will take $T_{en\_adc}f_{adc}$ samples. If that length of time is meaningful for the signal, say one symbol time of a modulation system, then you can justifiably say you are sampling that part of the signal at $f_{adc}$.

If however the signal is meaningful only over a larger time, then the dependence on $T_{loop}$ means you have a lower sampling rate.

In the simplest case, you can say your sampling rate is $1/T_{loop}$. This is the highest uniform sampling rate you can generally extract from your periods of samples/no samples.

If you have an underlying uniform sampling rate, and 'no sampling' during T_other consists of merely not taking those samples, then you may be able to extract a lower uniform sampling rate from the samples you have recorded. However, this doesn't sound like what you have, it sounds like the periods of sampling are asynchronous with respect to each other.

In the most complicated case, you can use a little known aspect of Nyquist sampling. Perfect reconstruction of a signal is theoretically possible if the mean sampling rate is above 2*bandwidth. This means you could, in theory, take the average sampling rate and use that to define your signal bandwidth. However, there are practical problems. Reconstruction from this sort of sampling is not supported by most signal processing toolboxes, and people are still writing PhD's on the best way to reconstruct signals from non-uniform samples. So you're on your own.

• [..] then you may be able to extract a lower uniform sampling rate from the samples you have recorded is there any chance to quantify this? That's actually what I am looking for. – user61801 Nov 27 '17 at 10:28