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| is it true, oscilloscope must reach at least 4x observed freq? |
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| Fungus:
--- Quote from: Someone on September 13, 2022, 03:15:08 am ---There are easily found examples of 2.5x being inadequate. --- End quote --- Please educate us. |
| tggzzz:
--- Quote from: David Hess on September 13, 2022, 12:15:14 am ---Bandwidth and sampling rate are completely independent. The sampling rate must meet the Nyquist criteria to accurately reconstruct the waveform, but this has nothing to do with the bandwidth as defined by the -3dB amplitude response, which is why equivalent time sampling works. As pointed out by tggzzz, a bandwidth limited signal can be reconstructed with a sampling rate greater than twice the bandwidth no matter where in the frequency spectrum it is, within the bandwidth of the sampler. The sampling function itself is equivalent to RF mixing, and the circuits can be identical. RF mixers make great microwave samplers when driven with a suitable pulse through their local oscillator port. The sampling part of an analog-to-digital converter can be modeled as a down-conversion mixer. --- End quote --- Precisely. A good practical example is the "Tayloe mixer" found in SDR receivers. Those irritate me. 40 years ago I built an 4kHz bandpass filter with a Q of ~4000 using 10% capacitors. It was based on the N-path filter concept I found in a 1950s BSTJ paper. The concepts were so counterintuitive that I had difficulty explaining them to analogue/RF engineers. They continued to fascinate me, I felt sure they would be useful in other ways, but had no professional reason to use them. After retiring I was just gearing up to playing with them again, and found Tayloe had "beaten me to it". Rats. |
| Fungus:
--- Quote from: David Hess on September 13, 2022, 12:15:14 am ---As pointed out by tggzzz, a bandwidth limited signal can be reconstructed with a sampling rate greater than twice the bandwidth no matter where in the frequency spectrum it is, within the bandwidth of the sampler. --- End quote --- In theory? Yes. In practical terms? Not so much. The reconstruction filter would become very unwieldy as you approach Nyquist. --- Quote from: Someone on September 13, 2022, 03:15:08 am ---I do this stuff for a living... you can keep putting out non-specific/vague figures but they are just that --- End quote --- I don't do it for a living but I've played around enough with digital audio synthesis to have confirmed the "2.5x limit" experimentally. ie. I've sat a potentiometer and manually dialed a frequency where I no longer observe the AM modulation effect mentioned earlier. The frequency I ended up with was right there in the 2.5x ballpark. Maybe it could have been 2.4x but it's definitely not as low as 2.2x. 2.5x may be a "non-specific/vague figure" but it works in practice. |
| nctnico:
--- Quote from: Fungus on September 13, 2022, 12:55:55 am --- --- Quote from: coppice on September 12, 2022, 11:56:35 pm ---You only need to sample at twice the bandwidth of the signal (or at one times the bandwidth for analytic sampling). --- End quote --- Completely false. Imagine a sine wave that you're sampling at exactly 2x frequency. a) You might sample the signal exactly on the peaks/troughs in which case you'll be fine. b) OTOH you might sample it exactly on the zero-crossing points, in which case you'll see nothing at all. You can also get every possible value in between (a) and (b), it's just dumb luck. If you sample at 99.99999% of Nyquist you'll drift slowly between (a) and (b) and see the amplitude varying on screen ("AM effect"). 2.5x Nyquist is the minimum to avoid this AM effect. --- End quote --- No. Coppice is right. Nyquist says that you'll have all the information in a signal up to fsample /2 (note: UP TO). You'll need lots of computational power to reconstruct the signal though in order to visualise it. Remember: an oscilloscope is there to visualise a signal. When the sampling is done the data in the buffer needs to be post-processed so the human brain can see and indentify the signal. The factor 2.5 is just a convenient factor where an oscilloscope can use relatively simple sin x/x reconstruction and doesn't need an utterly steep anti-aliasing filter. If you throw in more computational power, you can get much closer to 2 and digitally correct for the steep anti-aliasing filter. But since the amplitude error will already be large near the bandwidth of an oscilloscope, it isn't worth the effort. |
| robert.rozee:
just for a laugh, why don't we bring in some empirical data? a novel approach, i must confess, but do humour me just for a moment. 980Hz (approx) square wave of about 8v p-p. sampled at various sampling rates... 2000 sps (2x frequency): clearly this is a gross misrepresentation of the actual signal being measured! when data is scarce, a digital oscilloscope will default to showing a calming, un-contentious sine wave. 5000 sps (5x frequency): this is just weird - the oscilloscope is getting seriously fooled by the input signal. 10,000 sps (10x frequency): now we are starting to get there, although there is a whole load of waggling at top and bottom. 20,000 sps (20x frequency): the 'evil' version of 10x. 50,000 sps (50x frequency): starting to get there... 100,000 sps (100x frequency): wow... at 100x (!) we have a pretty good representation of the original signal. 200,000 sps (200x frequency): looks like the principal of diminishing returns has kicked in. 10M sps (10,000x frequency): and this is what the scope chose when the "Auto Setup" button was pressed. looks like the scope manufacturer knows best - at least in this case! cheers, rob :-) |
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