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采用在频域内具有极好紧支性和盒形特性的谐小波作为母小波,推导了基于离散谐小波变换的地震波时变谱,并给出了不同尺度下能量随时间变化的包络函数的近似解析表达式.文中以Northridge地震波为例分析了时频分布特征.研究发现,对于自振频率为f的结构,其地震反应与输入地震波的时变谱在f处的时域最大值(即maxt∈Tp[p(f,t)])以及地震波在f频率点附近的信号分量在时域内的能量集中程度有很大的关系;与db4小波基相比,利用谐小波作为母小波的小波变换,其频域具有较好的分辨率,但时域分辨率却较差.最后提出了两种基于离散谐小波逆变换的人工非平稳地震波仿真方法.
Using the harmonic wavelet with excellent compactness and box shape in the frequency domain as the mother wavelet, the time-varying spectrum of the seismic wave based on the discrete harmonic wavelet transform is deduced and the envelope function of the energy with time at different scales is given The paper analyzes the time-frequency distribution of Northridge seismic wave as an example. It is found that for the structure with natural frequency f, the time-domain maximum of the time-varying spectrum of seismic response and input seismic wave at f maxt∈Tp [p (f, t)]), and the degree of energy concentration in the time domain of the signal components near the f-frequency point of the seismic wave. Compared with the db4 wavelet base, wavelet using the harmonic wavelet as the mother wavelet Transform, the frequency domain has good resolution, but the time domain resolution is poor.Finally, two artificial non-stationary seismic wave simulation methods based on discrete harmonic inverse wavelet transform are proposed.