A method proposed by Salby for computing the zonal space-time Fourier transform asynoptically acquired satellite data has been tested and applied to soundings of brightness temperatures taken by polar-orbiting satellites. The technique, which yields the exact transform of the data with no distortions of fast-moving waves, is found to be robust under reasonable conditions of randomly varying signals, sampling errors and missing data points. In addition, when applied to measurements from instruments with multiple scan-tracks, a large number of latitudinally closely spaced spectra results, which enables one to average over latitude instead of or in addition to conventional frequency averaging to achieve greater statistical reliability and better signal-to-noise ratio. Some results of applying the method to real data are presented. Several well-known waves are identified, as well as two previously unreported small-amplitude spectral peaks corresponding to waves in the Southern summer stratosphere having wavenumber 7 and a period of 20.9-2.97 d westward, and wavenumber 6 with a period of 4.17-5.90 d eastward.