## 2 Materials and Methods
### Phase-Separation Technique  
In accordance with the aim of this study, particle and bubble velocities on two-phase bubbly flow can be identified separately by analyzing multi-frequencies and differences in amplitude of the Doppler signal. A technique based on the integration of time-frequency analysis and Doppler amplitude classification is proposed. This technique analyzes both the frequency and amplitude of the signal to decompose Doppler frequency of particle and bubble for obtaining the velocity of both phases separately. Several types of time-frequency estimator such as STFT, Gabor [25] and Wigner-Ville distribution (WVD) [26] can analyze time-frequency behavior of non-stationary signal which is the same kind of Doppler signal. Each type has advantage and disadvantage. Therefore, the performance of estimators must be evaluated before applying to the measurement system. The performance is evaluated in three indicators; Readability, Resolution and Computational time. The investigation was performed by using one Doppler signal obtained from two-phase bubbly flow as shown in Figure 5. Then, the signal was inputted to the algorithm of three estimators on LabVIEW software. Figure 6a-c are time-frequency spectrogram of Doppler signal obtained from STFT, Gabor and WVD, respectively. The evaluation of three estimators is shown in Tables 1 and 2. It can be concluded that Short-Time Fourier Transform has a good performance in three criteria (Readability, Resolution and Computational time). Therefore, STFT is selected to be time-frequency estimator in the phase-separation technique. The STFT analyzes the time-frequency effect of the Doppler signal. The classification of Doppler amplitude is performed by setting a threshold. The threshold value is based on the statistical data of Doppler amplitude reflected by particles and bubbles. The phase-separation technique is applied for operation in the UVP by replacing the frequency estimation section. Figure 7 demonstrates the process of the phase-separation technique. \[X(k,f_{D})=\sum_{n=0}^{N_{REP}-1}D(n)W_{n}(n-kS_{n})exp(-jn2\pi f_{D}) \tag{8}\]  
\[P(k,f_{D})=|X(k,f_{D})|^{2} \tag{9}\]  
The Doppler signal \(D(n)\) is in the form of complex discrete data extracted by the quadrature demodulation section is sent to STFT. The Doppler signal is divided into several windows, and each window is set to overlap with adjacent windows. The signal in each window is then transformed into the frequency spectrum along several short time periods. Its calculation is expressed in Equation (8) and the energy density of spectra at time \(k\) is denoted by Equation (9). It is called a time-frequency spectrogram, indicating time-frequency characteristics of the Doppler signal. Its characteristics depend on time step \(S_{n}\) and window length \(W_{n}\). In this study, for high time resolution, the time step was set equal to 1, and the window length for optimization was a crucial parameter for STFT as it governed the resolutions in both time and frequency. As the window length decreases, the time resolution increases but the frequency resolution in STFT decreases. Therefore, a shorter window length leads to spectral leakage. The methodology used to determine the optimum window length involves a comparison between the frequency analysis of STFT in each window length and the frequency setpoint (simulated signal). In this study, the setpoint value is determined from the Doppler frequency range at \(f_{PRF}\) 8 kHz. The maximum Doppler frequency is \(f_{Dmax}=f_{PRF}/2\). Therefore, the Doppler frequency range is 0-4 kHz. Figure 8 shows the results of the comparison. The optimum window length is 24. The spectrogram obtained from the STFT is sent to the peak detector. This section analyzes the energy peaks of the spectrogram. Each spectrogram peak value indicates the Doppler frequency data and time location at which the peak occurs. The information is provided in the form of array data--Doppler frequency (\(\mathbf{f_{D}}\)) and time location (\(\mathbf{t}\))--as expressed in Equation (10).