Hayashi, Y., 1982: Space-time spectral analysis and its applications to atmospheric waves. Journal of the Meteorological Society of Japan, 60 (1), 156-171.

Abstract: Space-time spectral analysis methods and their applications to large-scale atmospheric waves are reviewed.
Space-time spectral analysis resolves transient waves into eastward and westward moving components and is mathematically analogous to rotary spectral analysis which resolves two-dimensional velocity vectors into clockwise and anticlockwise components. Space-time spectral analysis can also resolve transient waves consisting of multiple wavenumbers into standing and traveling wave packets. Space-time energy spectra are governed by space-time spectral energy equations which consist of linear and nonlinear energy transfer spectra.
Space-time spectra can be estimated by either the lag correlation method, direct Fourier transform method or the maximum entropy method depending on the length of the time record. By use of the modified space-Fourier transform these spectra can be estimated correctly from polar-orbiting satellite data which are sampled globally at different hours of the day.
Space-time spectral analysis has been extensively applied to data generated by GFDL general circulation models to determine the wave characteristics, structure and energetics of transient planetary waves, to verify the model with observations and to clarify their generation mechanisms by means of controlled experiments.