# Envelop detection with low sample rate?

I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I don't need to reconstruct it, but to create an envelop detector from it, over time, based on lets say $1000T$ (periods).

So, over $1000$ periods of $3\textrm{ MHz}$, I will have: $300 \mu s/1.5 \mu s=200 \textrm{ samples}$. From these $200$ samples, I need to create some envelop detector, or continues curve to then later check if it has some large amplitude changes.

1. How can I chose where to sample the input signal so that I can get the "right points" of it- means mostly its maxes, where my sample rate is much slower then the signal ?
2. Should I use a moving average to get this curve ?
3. Is there another good approach expect from taking more periods?($>1000$)
• There is no way to solve your problem. Short of using a sampler with a faster rate, you'd have to filter the signal to reduce its bandwidth to ~300kHz, and hope you can learn what you need from that. – MBaz May 1 '16 at 18:28
• Really no way? Because 2 universities do exactly that with the same info exactly. – Curnelious May 1 '16 at 19:13
• What's your message bandwidth, also your detector's bandwdith, and cannot you implement a BandPass sampling strategy ? – Fat32 May 1 '16 at 19:52
• @Curnelious : Do you have links to the work by those universities that does this? – Peter K. May 6 '16 at 1:33
• @Curnelious : Is the signal a passband signal with min and max frequencies? Can you use the folding property while sampling? – oxuf Jun 4 '17 at 12:11

## 1 Answer

Is the ADC sample-and-hold fast enough to even capture any envelope peaks or even half cycles? If not, all bets are off.

If your ADC does have a fast enough capture time, then randomizing your sample times might be a good bet at capturing a few near extrema. If you know, a priori, the approximate shape of your waveform, then Monte-Carlo sampling might allow one to estimate the waveform amplitude from the statistical distribution of enough sufficiently time-randomized samples. Assuming the envelope changes slowly enough.

• Yes varying the sample intervals can extend your reach; I am not sure random is necessary but scanning might work: say 1.5 usec, 1.48 usec..3.2 usec can peak at different signals and might clarify your signal; if it doesn't change rapidly. Something analogous to dithering: trading bandwidth for resolution. I don't know of references though. The "fast enough" can be slightly relaxed to the edges being sharp enough. As far as I know an underutilized technique is to dither the edges of pixels to peek at finer details. Of course demodulation in both cases has to synchronized with the scan. – rrogers May 3 '16 at 22:05