The H-mode in tokamaks is characterized by the occurrence of large bursts of MHD activity at the plasma edge known as Edge Localized Modes (ELMs) causing particle and energy losses, which may result in a reduction of the energy confinement time as large as 20%. On the JET tokamak, Type-I and Type-III ELMs are seen in the edge Mirnov pickup coils as MHD events lasting from 200ms to 1ms. Such a short characteristic time scales involved in the growth and collapse of ELMs make the analysis of the temporal evolution of the amplitude and mode numbers of ELMs difficult to perform with the standard Fourier analysis. A spectral analysis designed for transients is required for such short-lived perturbations. We show in the present paper that the Morlet wavelet transform is one of the best options for investigating spectral properties of ELMs, including their toroidal mode numbers n, as time resolution comparable to the acquisition time can be achieved. We also compare the mode numbers n involved in ELMs with those of ELM pre-cursors and post-cursors also often observed on JET, which have a lifetime up to hundredths of ms, so that conventional Fourier analysis and the Morlet transform can be applied to them.