The space-time Fourier analysis technique proposed by Salby for asynoptic satellite data has been applied to brightness temperatures derived from Stratospheric Sounding Unit radiances from three months during the Southern Hemisphere winter. A series of peaks are observed in the spectra for wavenumbers 1 through 4 which travel eastward with the same phase speed. The wave 1, 4-day, and wave 2, 1.8-day, features observed have been described previously in the literature, and the existence of a wave 3, 1.2-day oscillation has also been reported. The current analyses provide corroborating evidence for these, using a different dataset and analysis technique, in addition to reporting a previously undetected wave 4, 0.8 day, feature. Twice-daily synoptic maps reconstructed from the transforms reveal, consistent with the findings of Prata, that these waves are components of one or more warm pools circling the pole with a period of about 3.8 days. These features exhibit sizable temperature perturbations (approximately 5 K) and long lifetimes in the upper stratosphere. One such pool retains its identity for at least seven complete revolutions around the pole.