No, I just meant that you get to pick the array of frequencies that the periodogram is sampled on. You can pick anything (that doesn't include f=0), so you could start with a coarse sampling to see where the major frequency content is. Then if the frequency content is constrained to one region, then you can choose a finer sampling of frequencies only within that band. That can save on computation costs if it's too expensive to do a fine sampling over the whole Nyquist range. But if it's cheap enough to do the fine sampling over the whole region, go ahead and do that.
I don't know of any work that apply's something like Welch's method per se to the LS periodogram, but if you squint, you can kind of see Welch's method as an ad hoc instance of a multitaper method, and there is a more rigorous application of multitaper methods to the LS periodogram. Not implemented in Python so far as I know, but there is an R implementation.
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Robert Kern