\label{fig:transform}
Fourier analysis of the meridional average (10$^{\circ}$S--10$^{\circ}$N) 500 hPa rotated meridional wind anomaly for a 30-day mean centered on 18 May 2006 (purple curve). Values outside of the region of interest (115$^{\circ}$E to 235$^{\circ}$E) have been set to zero. The individual Fourier components for wavenumbers 1--8 (grey dashed, with wavenumbers 5 and 6 highlighted in green) and the reconstructed signal from an inverse Fourier transform with wavenumbers 4--7 retained (dashed orange) and its corresponding wave envelope (solid orange) are all shown. The inset shows the amplitude of each of the individual Fourier components. 