In Fourier transforms, or periodograms, or signal processing in general, when you look at a time stream that is generated by a single frequency f (plus noise, say) and has a total time length T, you expect the power-spectrum ppeak, or the likelihood function for f to have a width that is no narrower than 1/T in the frequency direction. This is for extremely deep reasons, that relate to—among other things—the uncertainty principle. You can't localize a signal in both frequency and time simultaneously.
Ana Bonaca (Harvard) and I are fitting combs of frequencies to light curves. That is, we are fitting a model with K frequencies, equally spaced. We are finding that the likelihood function has a peak that is a factor of K narrower than 1/T, in both the central-frequency direction, and the frequency-spacing direction. Is this interesting or surprising? I have ways to justify this point, heuristically. But is there a fundamental result here, and where is it in the literature?
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