## 2 Experimental Setup and Processing Methods
### AVD Conversion Method  
Method 1 is called the Penzien filter, and it uses DFT and \(H_{2}(\omega)\)[32]. Method 2 uses the baseline correction and cosine correction filter [33]. Method 3 uses a least-square fitting and 4 th-order Butterworth filter [14]. The Penzien filter in Method 1 is a filtering process using the Fourier transform  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Equipment Name** & \begin{tabular}{c} **Model Name** \\ **(Manufacturer)** \\ \end{tabular}  & **Special Feature** & **Amount** \\ \hline \multirow{3}{*}{High-speed camera} & \multirow{3}{*}{\ \begin{tabular}{c} Phantom V641 \\ (Vision research) \\ \end{tabular}  } & As a device capable of shooting over 1000 frames per second, it captures moments that cannot be observed by the human eye and analyzes the behavior of the structure using these records. & Two sets \\ \hline \multirow{3}{*}{Target} & \multirow{3}{*}{ \begin{tabular}{c} Easy-to-perceive Quadrant target \& linear target \\ in TEMA software \\ \end{tabular}  } & 5 inch \\  & & & 3 inch \\ \cline{1-1}  & & & 3 inch \\ \cline{1-  
and transfer function, and it removes low-frequency noise by means of a high-pass filter. Method 2 computes the discrete data of the input seismic waves as the sum of the cosine functions by means of a cosine Fourier transform. In Method 3, the least-squares fitting implemented in the first step removes the linear drift in the acceleration. In this study, the long-term measurement of the acceleration of the high-rise building incorporates the error and drift of the baseline. This is the cause of some of the error in the measuring equipment, as well as the background noise. At this point, it is instructive to once again solve for the steady-state harmonic response using the exponential form of a solution. Consider the general case of harmonic loading expressed in exponential form:  
\[\ddot{v}(t)+2\xi\omega\dot{v}(t)+\omega^{2}v(t)=\frac{p_{0}}{m}\exp[i(\omega t +\phi)] \tag{1}\]  
where \(\phi\) is an arbitrary phase angle in the harmonic loading function, \(\omega\) is loading frequency, and \(\omega\) is natural frequency. In dealing with completely general harmonic loads, especially for the case of periodic loading where the earthquake is expressed as a series of harmonic terms, it is essential to define the input phase angle for each harmonic; however, this is usually most conveniently accomplished by expressing the input in complex number form rather than on the basis of amplitude and phase angle. In this section, only a single harmonic loading term will be considered; therefore, its phase angle is arbitrarily taken to be zero for the sake of simplicity. Therefore, it need not be included in the loading expression [32]. The specific solutions of Equation (1) and its first and second-time derivatives are  
\[v(t)=G\exp(i\omega t) \tag{2}\]  
\[\dot{v}(t)=i\omega G\exp(i\omega t) \tag{3}\]  
\[\ddot{v}(t)=-\omega^{2}G\exp(i\omega t) \tag{4}\]  
where \(G\) is a complex constant. To evaluate these, substitute Equations (2)-(4) into Equation (1), cancel out the common quantity, \(\exp(i\omega t)\), in each term, substitute \(\frac{k}{\omega^{2}}\) for m, and \(\beta\) for \(\frac{\omega}{\omega}\), and solve for \(G\), which yields  
\[G=\frac{p_{0}}{k}\bigg{[}\frac{1}{(1-\beta^{2})+i(2\xi\beta)}\bigg{]} \tag{5}\]  
\[G=\frac{p_{0}}{k}\bigg{[}\frac{1}{(1-\beta^{2})+i(2\xi\beta)}\bigg{]}=\frac{p_ {0}}{k}\bigg{[}\frac{1}{(1-\big{(}\frac{\omega}{\omega}\big{)}^{2})+2\xi\frac{ \omega}{\omega}}\bigg{]}=\frac{p_{0}}{k}\bigg{[}\frac{1}{\big{(}\frac{\omega ^{2}-\omega^{2}}{\omega^{2}}\big{)}+2\xi\frac{\omega}{\omega}\frac{\omega}{ \omega}}\bigg{]}=\frac{p_{0}}{k}\bigg{[}\frac{\omega^{2}}{\omega^{2}-\omega^{2 }+i2\xi\omega\omega}\bigg{]} \tag{6}\]  
Equation (5) is rearranged as Equation (7). \[\therefore G=\frac{p_{0}}{k}\bigg{[}\frac{\omega^{2}}{\omega^{2}-\omega^{2}+i2 \xi\omega\omega}\bigg{]} \tag{7}\]  
Rearranging Equation (4), we similarly obtain Equation (8).