2 ms·

> so you can’t tell between 2khz, 10khz, and 100khz Only when your sample rate is perfect! Let's say we have a 1GHz system, one instruction per Hz, a signal

> so you can’t tell between 2khz, 10khz, and 100khz Only when your sample rate is perfect! Let's say we have a 1GHz system, one instruction per Hz, a signal at 1MHz and we're measuring at 1kHZ. If we're rock-solid at 1kHz then, as you said, we can't distinguish 1MHz from 2kHz, but if we're off by a little bit, then things change. Let's say the 1MHz events are at times 50, 1050, 2050, and so on, and the 1kHz sample rate triggers at 0, 1000000, 2000000, and so on. You'll obviously never see that event. But suppose there's a little bit of noise in the sample rate timing and we're just under 1kHz, so now the samples are 0, 1000001, 2000001, 3000005, etc. Sooner or later we're going to hit that 1MHz event, and we're not going to hit it at the same rates as we would a 2kHz event, a 10kHz event, and so on. We might not hit it that often, but we'll hit it sooner or later, and we'll also hit a lot of its neighbors.

anonymous-panda 3y ago
You’re not describing anything different from how Nyquist pops up in analog signals either - sampling and signal will always have jitter and noise. I would recommend reading the linked pdf if you haven’t done so as it gives a number of examples of how Nyquist can screw up your intuition.
- bigbillheck 3y ago
  I read it when it was first posted, and skimmed it again just now to be sure, and my conclusion is unchanged: Nyquist has nothing useful to say about sampling profilers. I think the author would agree with me. See, for example, the discussion of EKG signals, or this bit from the intro: > The difficulty with the Nyquist-Shannon sampling theorem is that it is based on the notion that the signal to be sampled must be perfectly band limited. This property of the theorem is unfortunate because no real world signal is truly and perfectly band limited. whose relevance I'll get to below. (I'm assuming that by "sampling profiler" you mean the usual practice of recording on a cadence the call stack / program counter / etc of some code; if this is not what you meant please clarify) If you approach sampling profiling from a signals viewpoint, what's the signal that you're sampling? I see it as a collection of pulse waves of varying (and irregular!) duty cycles, each pulse wave corresponding to a yes/no answer to "is the program inside this function / executing this instruction / etc". At any given sample we collect our data and that tells us which waves are high; all others will be low. Nyquist, as the above quote points out, only applies to perfectly band limited signals. Not only are pulse waves not perfectly band limited, they're actually extremely not band limited, with energy at harmonics going all the way up. Right away that should tell you that Nyquist is the wrong way to be thinking about things! And furthermore, Nyquist tells you what you need if you want to reconstruct the original signal, but why do you want to do that in the first place? Do you actually care about the phase of the wave and the timings of the pulses, or do you just care about how often the wave is high? (i.e. how often any bit of code is executed). I don't think I've ever cared about the phase and timings when profiling, but I do care very much about how often the wave is high.

anonymous-panda 3y ago

You’re not describing anything different from how Nyquist pops up in analog signals either - sampling and signal will always have jitter and noise. I would recommend reading the linked pdf if you haven’t done so as it gives a number of examples of how Nyquist can screw up your intuition.

bigbillheck 3y ago
I read it when it was first posted, and skimmed it again just now to be sure, and my conclusion is unchanged: Nyquist has nothing useful to say about sampling profilers. I think the author would agree with me. See, for example, the discussion of EKG signals, or this bit from the intro: > The difficulty with the Nyquist-Shannon sampling theorem is that it is based on the notion that the signal to be sampled must be perfectly band limited. This property of the theorem is unfortunate because no real world signal is truly and perfectly band limited. whose relevance I'll get to below. (I'm assuming that by "sampling profiler" you mean the usual practice of recording on a cadence the call stack / program counter / etc of some code; if this is not what you meant please clarify) If you approach sampling profiling from a signals viewpoint, what's the signal that you're sampling? I see it as a collection of pulse waves of varying (and irregular!) duty cycles, each pulse wave corresponding to a yes/no answer to "is the program inside this function / executing this instruction / etc". At any given sample we collect our data and that tells us which waves are high; all others will be low. Nyquist, as the above quote points out, only applies to perfectly band limited signals. Not only are pulse waves not perfectly band limited, they're actually extremely not band limited, with energy at harmonics going all the way up. Right away that should tell you that Nyquist is the wrong way to be thinking about things! And furthermore, Nyquist tells you what you need if you want to reconstruct the original signal, but why do you want to do that in the first place? Do you actually care about the phase of the wave and the timings of the pulses, or do you just care about how often the wave is high? (i.e. how often any bit of code is executed). I don't think I've ever cared about the phase and timings when profiling, but I do care very much about how often the wave is high.