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is it true, oscilloscope must reach at least 4x observed freq?
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The Electrician:

--- 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 ---

Modern statements of the sampling theorem are sometimes careful to explicitly state that x(t) must contain no sinusoidal component at exactly frequency B, or that B must be strictly less than ½ the sample rate.
Someone:

--- Quote from: The Electrician on September 13, 2022, 02:23:23 am ---
--- 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 ---
Modern statements of the sampling theorem are sometimes careful to explicitly state that x(t) must contain no sinusoidal component at exactly frequency B, or that B must be strictly less than ½ the sample rate.

--- End quote ---
and to be more clear, 2.5x is a figure that provides some non-specific limit to that effect under typical band limiting/anitaliasing/reconstruction and does not ensure errors are avoided.

We dont have perfect sampling, or prefect band limited signals, or perfect reconstruction, and they all contribute (among other things) even in pure digital or simulation.
Fungus:

--- Quote from: Someone on September 13, 2022, 02:33:56 am ---and to be more clear, 2.5x is a figure that provides some non-specific limit to that effect under typical band limiting/anitaliasing/reconstruction and does not ensure errors are avoided.

--- End quote ---

I don't think you can get major distortions at 2.5x with a band-limited signal, but that's still an "if". How would you know?

Workaround: Use as few channels as possible on your DSO to keep the sample rate as high as possible. If in doubt, turn channels on/off to see if the signal of maximum interest changes shape.
Someone:

--- Quote from: Fungus on September 13, 2022, 02:59:00 am ---
--- Quote from: Someone on September 13, 2022, 02:33:56 am ---and to be more clear, 2.5x is a figure that provides some non-specific limit to that effect under typical band limiting/anitaliasing/reconstruction and does not ensure errors are avoided.
--- End quote ---
I don't think you can get major distortions at 2.5x with a band-limited signal, but that's still an "if". How would you know?
--- End quote ---
Because I do this stuff for a living... you can keep putting out non-specific/vague figures but they are just that, something which might be true in some non-specified situation.

There are easily found examples of 2.5x being inadequate.
The Electrician:

--- Quote from: Someone on September 13, 2022, 03:15:08 am ---
--- Quote from: Fungus on September 13, 2022, 02:59:00 am ---
--- Quote from: Someone on September 13, 2022, 02:33:56 am ---and to be more clear, 2.5x is a figure that provides some non-specific limit to that effect under typical band limiting/anitaliasing/reconstruction and does not ensure errors are avoided.
--- End quote ---
I don't think you can get major distortions at 2.5x with a band-limited signal, but that's still an "if". How would you know?
--- End quote ---
Because I do this stuff for a living... you can keep putting out non-specific/vague figures but they are just that, something which might be true in some non-specified situation.

There are easily found examples of 2.5x being inadequate.

--- End quote ---

Please give us some examples where 2.5x is inadequate.  :)
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