  In Patil et. al 2024a, we developed a multitaper power spectrum estimation
method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and
showed that it not only improves upon the statistical issues of the
Lomb-Scargle periodogram, but also provides a factor of three speed up in some
applications. In this paper, we combine mtNUFFT with the harmonic F-test to
test the hypothesis that a strictly periodic signal or its harmonic (as opposed
to e.g. a quasi-periodic signal) is present at a given frequency. This
mtNUFFT/F-test combination shows that multitapering allows detection of
periodic signals and precise estimation of their frequencies, thereby improving
both power spectrum estimation and harmonic analysis. Using asteroseismic
time-series data for the Kepler-91 red giant, we show that the F-test
automatically picks up the harmonics of its transiting exoplanet as well as
certain dipole ($l=1$) mixed modes. We use this example to highlight that we
can distinguish between different types of stellar oscillations, e.g.,
transient (damped, stochastically-excited) and strictly periodic (undamped,
heat-driven). We also illustrate the technique of dividing a time-series into
chunks to further examine the transient versus periodic nature of stellar
oscillations. The harmonic F-test combined with mtNUFFT is implemented in the
public Python package tapify (https://github.com/aaryapatil/tapify), which
opens opportunities to perform detailed investigations of periodic signals in
time-domain astronomy.
