We investigate the intra-annual variability of the tropical Atlantic Ocean from 20°S to 20°N with weekly satellite altimetric Absolute Dynamic Topography data from 1992 to January 2011 at 1/3° grid resolution. This data set is analysed with Empirical Orthogonal Function methods, and three regions of high variability are found. The first region, between 3°N and 11°N, is characterised by the presence of strong eddies linked to the North Equatorial Counter Current retroflection in the vicinity of the Brazilian coast. In the second region, we observed the presence of instability waves centered at 4°N between 40°W and 10°W. The third region, between 3°S and 3°N is characterised by the presence of Kelvin waves at the Equator, and Rossby waves at 3°S and 3°N. We explore the characteristics of these waves with Hilbert transform based methods. These techniques allow us to estimate the instantaneous amplitude, period, and speed of the propagations. We show that these quantities are correctly estimated, and are physically valid if the signals are asymptotic, and are decomposed in their high (from 2 to × 8 weeks), and low (from × 8 to 52 weeks) frequency asymptotic components. For this purpose we develop a filtering technique based on the Empirical Mode Decomposition method. The estimated mean speeds of the propagating waves are 19 cm/s, for the eddies close to the Brazilian coast, 50 cm/s, for the instability waves at 4°N, 181 cm/s, for the Kelvin waves at the Equator, 61 cm/s for the Rossby waves at 3°N, and 48 cm/s at 3°S. All of these waves are characterized by the presence of a strong annual cycle in their instantaneous amplitude, period, and speed.