Transient backscattering from a spherical target under incidence of an electromagnetic short pulse is studied. The target can be a perfectly conducting sphere, a dielectric sphere or a dielectric spherical shell. To understand the scattering mechanism from transient impulse echoes for target detection, both the short-time Fourier transform(STFT) and the wavelet transform (WT) are applied to retrieval of scattering information from the backscattering data. Analysis in both the time and frequency domains demonstrates that the WT is more feasible than the STFT to clarifying scattering process of the scatterer because of its excellent multi-resolution characteristic. This technique shall be helpful for scattering analysis and detection of more complex single or multi-targets.