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Why don't we use the frequency domain for o11y stuff? Intuitively it seems like being aware of periodic phenomena, and being able to identify them, would be useful. But nobody does it. Is that because it's actually useless or some other reason?

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Frequency domain analysis is useful when you have a physical quantity (which normally comes down to energy or power, in joules or watts) that you want to understand in terms of frequency. Mere periodicity of events doesn't imply that is the case. Statistical techniques, on the other hand, are widely applicable to time series data.

I guess I'm thinking along the lines of analyzing processes for which I have some intuition what the frequency distribution should look like. Say I have a scheduled task running once per second which does some work, and I expect to see a corresponding cpu spike every second. But I notice that sometimes when the task runs it takes longer. Looking at the cpu spectrum I see a frequency spike at 1Hz corresponding to my 1/s task, but I also see a spike at 0.2Hz, confirming my suspicion that something is contending for cpu resources on every fifth task, slowing it down. Now I know to look for something that's happening every 5s.

In this contrived example I could have probably intuited that I was looking for something with a period of 5s without looking at the spectrum but maybe there are cases where it could be useful? I guess I'll just have to play around with data and find out :p.

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