Estimation of earthquake frequency content and its effect on dynamic analysis using continuous and discrete wavelet transform

Wavelet transform is one of the mathematical concepts for studying the frequency content of waves. It can be divided into two groups, continuous and discrete. In general, the continuous wavelet transform is used to examine the time-frequency relationship, whereas the discrete wavelet transform is used for filtering and noise reduction in waves. In this paper, for the first time, the combination of these two concepts is used for the earthquake acceleration wave. For this purpose, eight earthquakes from four different locations in the world have been selected. Initially, each earthquake is filtered up to 5 stages using a discrete wavelet transform. At each stage of the filter, two waves of approximations and details are obtained. Due to the close approximation of the frequency content of the wave to the original earthquake, the approximate wave is used for subsequent calculations. The Fourier spectrum and the diagram of five of the dominant frequency of the earthquake are plotted in the next step. Also, using the continuous wavelet transform, the time-frequency curves of the main earthquakes and the time-frequency curves of the wave obtained from the discrete wavelet transform are investigated. The goal was to find the best stage of a discrete wavelet filter based on frequency content to reduce computations by more than 80%. The time of the strong ground motion, the structural response of a single degree of freedom, and the dynamical response of the timing of the structure of a degree of freedom are all investigated in the following step. By examining the above parameters, the best-performing wavelet transformation step is inferred. (c) 2022 Sharif University of Technology. All rights reserved.