Long-term evolution of a narrow-banded nonlinear wave train is investigated experimentally. The wavelet analysis providing information in both time and frequency domain is employed to examine the local evolutionary characteristics of wave modulation. The zero-crossing method, Hilbert transform and Fourier transform are utilized to compare and validate the results obtained from the wavelet analysis. Results show that the modulated wavetrain resulting from the sideband instability can be represented by the peak frequencies in the wavelet spectrum. The local evolutionary properties of asymmetric amplitude and frequency modulations are found. The local frequency downshift is evidenced to correlate to the wave breaking. It is manifested that the energy of the waves near the front of modulated wave group is originally concentrated near the upper sideband and then is downshifted to the lower sideband after the occurrence of wave breaking and the wave fusion.