Since you've already looked at this problem a fair amount and done some optimization, further improvements are likely to depend on the partiulars. Thus there are naturally some quick questions right off. Mine have to do with your saying
it needs to be really fast.
I'm assuming this has to be fast because it's run again and again, on successive data sets. Thus compile time is irrelevent to performance.
Does the spectrum change from call to call, or can one prep the spectrum once and run a bunch of subspectra against it. If so, how many subspectra for each spectrum.
What's the dynamic range of the data. What's the data's precision. Are these things that can be determened once, entered once in advance of each run, or maybe they can't be determined at all in advance. (Solving things in the more general case can be way more expensive that solving a more particular problem, which is why engineering thinking is so different from mathematics. The mathematics ignores the boundary conditions, engineering often starts with them.)
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