## 2 Methods  
The noise separation technique using the phase conjugation method proposed in this paper is divided into reconstruction of noise source information using the phase conjugation method and calculation of noise signal separation based on the equivalent point source method. Figure 1 illustrates the process of the noise separation technique using phase conjugation:1. A microphone line array is constructed to measure the complex sound pressure \(p(r,\omega)\) and its gradient \(\frac{\partial p(r,\omega)}{\partial n}\) whose units are both dBA of the sound field generated by noise sources, where \(r\) is the position of line array with a unit m; \(\omega\), whose unit is rad/s, is the circular frequency; and n is the normal unit vector of microphone line array. 2. The complex sound pressure and its gradient are processed by the phase conjugation method to obtain sound pressure amplitude and phase information of each noise source, where the ratio of the sound pressure amplitude is the noise source intensity ratio \(s_{1}:s_{2}:\cdots:s_{m}\) with 1 unit, and the opposite of the sound pressure phase value is the initial phase value of the noise source \(\theta_{i},\ i=1,2,\cdots,m\) with rad unit. 3. The sound pressure amplitude \(p_{0}\) (dBA) of the points to be separated is measured by microphones placed at these points. 4. Sound pressure separation results \(p_{i},\ i=1,2,\cdots,m\) (dBA) of each source at the points to be separated are obtained by calculating the values in the 2 nd and 3 rd steps using the equivalent point source method. The core methods used in the separation technique illustrated in Figure 1 are described below, and they mainly include how to measure complex sound pressure and its gradient, the phase conjugation method, and the equivalent point source method. 1. How to measure the complex sound pressure and its gradient  
A microphone array is used to measure the steady-state sound pressure spectral signals of the radiated sound field of noise sources, and a reference microphone is fixed near the noise sources to measure the steady-state sound pressure spectral signal. The complex sound pressure of the radiated sound field of a noise source is:  
\[p=|p|\exp(\mathrm{i}(\omega t+\theta)), \tag{1}\]  
where \(|p|\) is the sound pressure amplitude obtained by self-spectral analysis of the array microphone \(|p|=\sqrt{P_{a}P_{a}^{*}}\); \(\theta\) is the relative phase obtained by cross-spectral analysis between the array and reference microphone \(\theta=\arctan(P_{r}P_{a}^{*})\); \(P_{a}\) and \(P_{r}\) are, respectively,  
Figure 1: Process of noise separation technique using phase conjugation method. sound pressure measured by the array and reference microphones; * is the symbol of complex conjugation; i is the imaginary unit; and \(t\)(s) is the time. The sound pressure amplitude and phase can be obtained through above operations, and then the complex sound pressure and its gradient can be obtained by 3 steps. Firstly, the complex sound pressure \(p_{1}\) of the noise source at the measuring microphone array location is measured. Secondly, the measuring microphone array is moved forward or backward by 1 cm and complex sound pressure \(p_{2}\) at the present array location. Finally, the final sound pressure is equal to the mean of \(p_{1}\) and \(p_{2}\),\(p=(p_{1}+p_{2})/2\), and the final sound pressure gradient is equal to \(\frac{\partial p}{\partial n}=(p_{2}-p_{1})/\Delta d\) where \(\Delta d=1\) cm. 2. Phase conjugation method  
The reason that the time reversal method can realize the reverse propagation and adaptive focusing of acoustic waves is that \(p(r,t)\) and \(p(r,-t)\) are both solutions of the line acoustic wave equation \(\ddot{p}=c_{0}^{2}\
abla^{2}p\) where \(c_{0}\) (m/s) is sound velocity of a medium. Time reversal in the time domain is equivalent to the phase conjugation in the frequency domain, i.e., \(p(r,t)\) and \(p(r,-t)\) are equivalent to \(p(r,\omega)\) and \(p^{*}(r,\omega)\)[14].