## 2 Materials and Methods
### Target Signal Detection and Marking Experiment  
Marine background noise is generated by geological activities, engineering machinery activities, sea surface winds and waves, biological activities, etc. After long-distance propagation through the seawater, these components overlap with each other, forming a complex high-intensity noise with a wide frequency band. It is necessary to denoise the original data before detection and marking. The loss function of sound propagation in the sea can be written as  
\[PL=20\mathrm{lg}r+ar\times 10^{-3}, \tag{4}\]  
where \(PL\) is the loss of the sound; \(r\) is the propagation distance; and \(a\) is the sound loss coefficient in the sea, which has a positive correlation with the frequency. In accordance with this function, the loss of sound has a positive correlation with the frequency and propagation distance. Although marine background noise is distributed throughout the whole frequency band, the energy is concentrated in the low-frequency band.  
Figure 3: Resolutions of STFT and WT.  
Low-frequency noise can be filtered out using a high-pass filter or band-pass filter. A high-pass filter can filter out signals lower than the cut-off frequency. A band-pass filter can filter out non-specified frequency-band signals. Since the high-frequency characteristic is sufficient for detection, it is not necessary to retain the low-frequency band. Therefore, the Butterworth high-pass filter was selected to filter out all the signals lower than the cut-off frequency. This filter can ensure that the frequency response curve for the passband is as flat as possible so that the frequency response curve for the stop band gradually drops to zero. The function of the Butterworth high-pass filter can be written as  
\[\left|H(\omega)\right|^{2}=\frac{1}{1+(\frac{\omega\cc}{\omega^{\prime}})^{2 }}, \tag{5}\]  
Figure 4: Time–frequency spectra provided by STFT and WT. (**a**) Spectrum calculated by STFT. (**b**) Spectrum calculated by WT.  
where \(n\) is the order of the filter, and \(\omega_{\rm C}\) is the cut-off frequency. The filter \(H(\omega)\) is approximately equal to 1, preserving the signal when the frequency \(\omega\) is higher than \(\omega_{\rm C}\). The cut-off frequency was set to 1 kHz for click detection and 0.1 kHz for whistle and burst pulse detection. The hydrophone, after filter application, was input into the procedure shown in Figure 1.  
The time-frequency data obtained with STFT or WT represent a three-dimensional matrix \(E^{t\times f}\), where \(t\) represents the position on the time axis, and \(f\) represents the position on the frequency axis. The set signal strength parameter \(M_{\rm e}\), \(M_{\rm e}\) can be calculated with  
\[M_{\rm e}=\sum_{f_{\rm min}}^{f_{\rm max}}fe_{(t,f)}, \tag{6}\]  
Next, we set a lower threshold \(T_{e}\). The signal at \(t\) can be considered as part of the target signal when \(M_{\rm e}>T_{\rm e}\). As shown in Figure 1, we obtain \(M_{\rm e}\) at the moment \(t\). It is considered that the data at moment \(t\) do not belong to the target signal if \(M_{\rm e}<T_{\rm e}\), setting the non-signal mark \(a_{\rm t}=t\), while the signal mark \(b_{\rm t}\) remains unchanged. It is considered that the data at moment \(t\) belong to the target signal if \(M_{\rm e}>T_{\rm e}\), setting the signal mark \(b_{\rm t}=t\). If \(a_{\rm t}=t-1\), the current moment is the starting point of the suspected signal, setting the signal starting mark \(u=t\). If \(a_{\rm t}\
eq t-1\), \(b_{\rm t}=t-1\). The current moment is the end point of the suspected signal, setting the signal ending mark as \(v=t\). Setting the duration mark \(M_{\rm t}\), \(M_{\rm t}\) can be calculated as:  
\[M_{\rm t}=v-u, \tag{7}\]  
where \(v\) is the end moment of a signal, and \(u\) is the starting moment of a signal. Then, we set an upper limit of duration \(M_{\rm max}\) and lower limit of \(M_{\rm min}\). If \(M_{\rm t}\in(M_{\rm min},M_{\rm max})\), it is determined that the signal belongs to the target signal.