  We used 22 $\mu$m (W4) Wide-field Infrared Survey Explorer (WISE)
observations of 4420 asteroids to analyze lightcurves and determined spin
period estimates for 1929 asteroids. We fit second-order Fourier models at a
large number of trial frequencies to the W4 data and analyzed the resulting
periodograms. We initially excluded rotational frequencies exceeding 7.57
rotations per day (P < 3.17 hr), which are not sampled adequately by WISE, and
periods that exceed twice the WISE observation interval, which is typically 36
hr. Three solutions accurately capture the vast majority of the rotational
frequencies in our sample: the best-fit frequency and its mirrors around 3.78
and 7.57 rotations per day. By comparing our solutions to a high-quality
control group of 752 asteroid spin periods, we found that one of our solutions
is accurate (within 5%) in 88% of the cases. The best-fit, secondary, and
tertiary solutions are accurate in 55%, 27%, and 6% of the cases, respectively.
We also observed that suppression of aliased solutions was more effective with
non-uniform sampling than with quasi-uniform sampling.
