In this article, the discrete wavelet transform (DWT) has been used to construct the wavelet response spectrum analysis (WRSA) of structures in the linear elastic zone. For this purpose, the elastic response spectra of different single degree of freedom (SDOF) systems are studied for different beam-to-column stiffness ratios. Initially, using the DWT, the records of near- and far-field earthquakes are decomposed into three levels. Finally, the linear response spectra of the SDOF systems are constructed subjected to the main and decomposed earthquakes. In the end, the error values for different levels of decompositions are computed using the considered error estimation criteria. The results show that using WRSA, the computational volume of time history analysis has reduced since the consuming time to perform the analysis has significantly reduced (e.g., it reduces the computational cost by almost 50% in the first decomposition level). In addition, the results indicate that the highest error values occur for the structures with a beam-to-column stiffness ratio equal to one. However, for the structures with ratios of greater than one, the values of error reduced. For the conventional structures where the ratio is less than one and the natural period is in the range of 0.5 s and 10 s, the error values are <10%. Results also revealed that, except for the structures with beam-to-column stiffness ratio equal to one, in all the other cases, the values of error for the structure subjected to the near-field earthquakes are less than those of the far-field ones. Furthermore, the results obtained from the SDOF system analysis were investigated for several multi-degree-of-freedom structures with a linear behavior.

在本文中，离散小波变换（DWT）已用于构造线性弹性区域中结构的小波响应谱分析（WRSA）。为此，针对不同的梁柱刚度比，研究了不同单自由度（SDOF）系统的弹性响应谱。最初，使用DWT将近场和远场地震的记录分解为三个级别。最后，构造SDOF系统的线性响应谱，使其经受主要地震和分解地震。最后，使用考虑的误差估计标准来计算不同分解级别的误差值。结果表明，使用WRSA，时间历史分析的计算量减少了，因为执行分析的时间大大减少了（例如，在第一分解级别上，计算量减少了近50％）。此外，结果表明，梁柱刚度比等于1的结构出现最高的误差值。但是，对于比率大于1的结构，误差值会减小。对于比率小于1且自然周期在0.5 s和10 s范围内的常规结构，误差值<10％。结果还表明，除了梁柱刚度比等于1的结构外，在其他所有情况下，遭受近场地震的结构的误差值均小于远场地震的结构。那些。