Power spectral density estimation of seismic wave based on wavelet transform

Understanding and cognition on characteristics of earthquake ground motion is the foundation and precondition of structural response analysis. Traditional Fourier amplitude spectrum and power spectral density(PSD) representations based on Fourier transform have limitations, that is, it loses any information related to time and is unable to completely reflect the non-stationary characteristics of earthquake essentially. Wavelet transform possesses excellent signal processing capability in both time domain and frequency domain, so it can reflect the non-stationary characteristic more precisely. Utilizing the band pass character of wavelet transform, the relations between wavelet coefficients and power spectral density on different frequency bands are deducted, in addition, PSD estimate method and time-dependent PSD estimate method based on wavelet transform are also presented in this paper. The feasibility of the presented method is illustrated by an example.