﻿ 基于双树复小波的被动目标特征提取方法研究
 舰船科学技术  2016, Vol. 38 Issue (11): 102-105 PDF

Research on feature extraction for passive target based on dual-tree complex wavelet transform
XU Chuan, HU You-feng, XU Wei
Kunming Precision Machinery Research Institute, Kunming 650101, China
Abstract: Due to the difficulty in feature extraction of underwater target radiated noise, a novel method based on dual-tree complex wavelet transform (DT-CWT) is presented. Firstly, a modified method based on wavelet threshold de-noising is applied to reduce the noise from the signal and shows a better de-noising performance. Secondly, DT-CWT is introduced during feature extraction to calculate the feature vectors and the results are almost invariant even if the signal is shifted in time domain. The experiment results of simulation signal and the real underwater acoustic signal show that the method shown in this paper can get more stable feature vectors than discrete wavelet transform (DWT).
Key words: underwater target radiated noise     wavelet de-noising     dual-tree complex wavelet transform (DT-CWT)     feature extraction
0 引言

1 小波阈值降噪及其原理

1）选择合适的小波并确定小波分解的层次N，对信号进行N层小波分解；

2）对从第1层到第N层的每一层高频系数，选择一个阈值进行阈值量化处理；

3）根据小波分解第N层的低频系数和经过量化处理后的第1层到第N层的高频系数，对一维信号进行小波重构。

 $t{h_j}={\sigma _{n, j}}\sqrt {2 \cdot \ln(\frac{N}{{{2^j}}})}, {\sigma _{n, j}}=\frac{{Median\{ |{\upsilon _{j, n}}|\} }}{{0.6745}}.$

 $\eta(x, th, m)=\left\{ \begin{array}{l} x - 0.5 \cdot th \cdot {\rm{sign}}(x)|x| > th, \\ 0.5 \cdot k \cdot th \cdot \tan(\frac{{{\rm{\pi }} \cdot x}}{{4 \cdot th}})|x| \le th. \end{array} \right.$ (1)

 $f(n)=\sum\limits_{i=8}^{11} {\sin(2 \cdot {\rm{ \pi }} \cdot i \cdot n/220)} {\mkern 1mu} {\mkern 1mu} {\rm{.}}$ (2)

2 基于双树复小波变换的能量特征提取

1）对原始信号进行双树复小波分解，得到各层信号的小波系数；

2）对高频的小波系数进行重构，得到重构的各层信号；

3）求高频各层信号的能量Ei(i=1, 2, ...)，其中 ${E_i}=\sqrt {\sum\limits_{k=1}^n {{{\left| {{S_j}(k)} \right|}^2}} }$

4）构造特征向量。

 $\text{特征向量}\quad { \boldsymbol{T}}=\left[{\frac{{{E_1}}}{E}, \frac{{{E_2}}}{E}, \frac{{{E_3}}}{E}, \frac{{{E_4}}}{E}, ...} \right] \text{，}$ (5)

3 应用分析

3.1 实验仿真

 ${s_i}(n)=\sum\limits_{k=1}^{{K_i}} {{a_{ik}}\sin } \left\{ {{k_i}\left[{2{\rm{\pi }}{f_i}n{T_s}+{\varphi _i}(n)} \right]+{\gamma _{ik}}} \right\}.$ (4)

 图 1 仿真的舰船辐射噪声信号及其频谱 Fig. 1 Simulation of ship radiated noise and its spectrum

 图 2 去噪后的舰船辐射噪声信号及其频谱 Fig. 2 Ship radiated noise and its spectrum after noise reduction

3.2 实航数据验证

 图 3 原始信号的双树复小波重构信号 Fig. 3 Reconstruction signals of original signal using DT-CWT

 图 4 原始信号的离散小波变换重构信号 Fig. 4 Reconstruction signals of original signal using DWT

 图 5 时移信号的双树复小波变换重构信号 Fig. 5 Reconstruction signals of shifted signal using DT-CWT

 图 6 时移信号的离散小波变换重构信号 Fig. 6 Reconstruction signals of shifted signal using DT-CWT

 图 7 不同时移信号的特征向量（离散小波变换） Fig. 7 Feature vectors of different shifted signals using DWT

 图 8 不同时移信号的特征向量（双树复小波变换） Fig. 8 Feature vectors of different shifted signals using DT-CWT

4 结语

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