  The presence of oscillations in aggregated COVID-19 data not only raises
questions about the data's accuracy, it hinders understanding of the pandemic.
Spectral analysis is used to reveal additional properties of the data, and the
oscillations are replicated using sinusoidal resynthesis. The precise behavior
of the seven-day moving average is also discussed, specifically, the cause of
its jaggedness and the phase error it introduces. In comparison, other
filtering techniques and Fourier processing produce superior smoothing and have
zero phase error. Both of these are presented, and they are extended to isolate
several frequency ranges. This extracts some of the same short-term variability
that is resynthesized, and it shows that fluctuations with periods between 8
and 21 days are present in U.S. mortality data. These methods have applications
that include modeling epidemiological time-series data as well as identifying
less obvious properties of the data.
