Instantaneous frequency and wave mode identification in a magnetosheath using few spatial points

Observational data such as those obtained from the magnetosheath in the downstream of Earth's bow shock have waveforms that differ from those of sinusoidal signals. In practice, they are not even aggregates of sinusoidal signals. Therefore, the frequency decomposition for the data requires technique that will account for the time-varying features of the data that will lead to deduction of physical meaning of the observations. The combination of empirical mode decomposition (EMD) and Hilbert transform has been used for extracting the various contributing oscillatory modes (EMDs) and the instantaneous frequency determination (Hilbert transform) of every physically meaningful mode called intrinsic mode function (IMF). The resulting instantaneous frequencies are used to determine instantaneous wave vectors. The combination of the instantaneous frequencies and wave vectors is useful in the identification of wave modes based on the characteristics of the waves. The results show that EMD-Hilbert can be more reliable than simple Hilbert transform alone.