## 3 PNCC Method Based on Wavelet Packet Transform
### Improved PNCC Method Based on Wavelet Package  
The specific calculation process of the original PNCC algorithm can be divided into the following steps: audio signal front-end processing, temporal integration for environmental analysis based on asymmetric noise suppression, mean power normalization and nonlinear processing. In this study, the first part of the original PNCC algorithm is improved. The overall framework of the algorithm is as follows (Figure 4). In the audio front-end processing of the original PNCC method, it is often necessary to pre-emphasize the sampled speech signal in the form of \(H(z)=1-0.97z^{-1}\). Here, we can understand this as a high-pass filter. Specifically, this is to remove the effect of lip radiation and increase the high-frequency resolution of speech. However, in this study, the audio data frequency distribution of a trunk borer is mainly concentrated in the vicinity of 70, 1500 and 1850 Hz. There is almost no audio component of trunk borer's in 400 -800 Hz and a frequency band higher than 2400 Hz. Therefore, if the pre-emphasis processing method of speech signal is used, the audio component of trunk borer around 70 Hz will be ignored and the high-frequency noise between 2400 and 4000 Hz will be amplified. Another reason for this is that there is no lip radiation effect in this study, so we remove the pre-emphasis part of the original algorithm. After pre-weighting, the original PNCC algorithm uses short-time Fourier transform and a 40-channel Gammatone filter with equivalent rectangular bandwidth center frequency between 200 and 8000 Hz, and the output results are processed in a short- and medium-time, respectively. In this study, we use wavelet packet transform to replace the short-time Fourier transform in the original method. Compared with short-time Fourier transform, wavelet packet transform develops the localization advantage of short-time Fourier transform and overcomes the disadvantage of constant window function, so it is an effective method for non-stationary signal analysis and feature extraction. The duration of the audio data used  
Figure 3: This picture shows the audio signal and its frequency spectrum of trunk borer’s in harsh acoustic environment. in the study is about 20 s, while the audio signal duration of trunk borer is about 15-20 ms (as shown in Figure 2). From Section 3.1, we know that the trunk borer audio is not easy to observe over a long period of time, so we retain the framing processing and make the frame length close to the duration of the trunk borer audio as possible. Then, the wavelet packet coefficients are obtained by using the three-layer wavelet packet transform in the time-frequency domain, and the low-frequency and high-frequency parts of the spectrum are spliced in the order from low to high. Next, according to the audio frequency range of trunk borers, we adjust the center frequency range of the equivalent rectangular bandwidth of Gammontone filter bank to 50-4000 Hz. Considering that the energy of speech and signals of trunk borers are more concentrated than noise and reverberation signals, we retain the original PNCC method in temporal integration for environmental analysis based on asymmetric noise suppression, mean power normalization and nonlinear processing. The details are as follows. First of all, the short-term power of PNCC is calculated according to the spectrum. The short-term power of the PNCC feature is defined as follows  
\[P[m,l]=\sum_{k=0}^{(K/2)-1}\left|X\left[m,e^{i\omega_{k}}\right]H_{l}\left(e^{ i\omega_{k}}\right)\right|^{2} \tag{1}\]  
where \(K\) represents the length of STFT transform, \(m\)and \(l\) represent input data frame number index and gammontone filter channel index. \(P[m,l]\), \(X[m,e^{i\omega_{k}}]\), and \(H_{l}(e^{i\omega_{k}})\) represent the  
Figure 4: Proposed method flowchart. short-term power, the frequency response of the input data and the frequency response of the Gammontone filter of the index, respectively.