CN103840893B - Ping reconstructing method under a kind of underwater sound multi_path channel - Google Patents

Abstract

Translated fromChinese

本发明提供的是一种水声多途信道下声脉冲信号重构方法。(1)将信道输出信号经过卷积同态特征系统，将信号从时域转换到复倒谱域；(2)利用基于尖峰搜索思想构建复倒谱域滤波器并进行滤波，即根据信道的复倒谱特性，在复倒谱域上采用尖峰搜索的方法自动搜寻多途尖峰脉冲并对其进行平滑处理，从而实现复倒谱多途干扰的滤除；(3)将滤波后的结果经过卷积同态逆特征系统，实现声脉冲信号的重构。本发明的方法具有无需信道或信号参数等先验知识、适用于快变信道、特征滤波器构建方法简易、重构误差小等特点。

The invention provides a method for reconstructing an acoustic pulse signal in an underwater acoustic multi-channel channel. (1) Pass the channel output signal through the convolution homomorphic feature system, and convert the signal from the time domain to the complex cepstral domain; (2) use the peak search idea to construct a complex cepstral domain filter and perform filtering, that is, according to the channel Complex cepstrum characteristics, using the peak search method in the complex cepstrum domain to automatically search for multi-channel spikes and smooth them, so as to realize the filtering of complex cepstrum multi-channel interference; (3) The filtered results are passed through Convolution homomorphic inverse eigensystem to realize reconstruction of acoustic pulse signal. The method of the invention has the characteristics of no need for prior knowledge of channel or signal parameters, etc., applicable to fast-changing channels, simple construction method of characteristic filter, small reconstruction error and the like.

Description

Translated fromChinese

一种水声多途信道下声脉冲信号重构方法A Reconstruction Method of Acoustic Pulse Signal in Underwater Acoustic Multi-channel Channel

技术领域technical field

本发明涉及的是一种水声信号处理技术方法，具体涉及水声多途信道中的多途影响抑制及声脉冲信号重构的方法。The invention relates to an underwater acoustic signal processing technology method, in particular to a method for suppressing multi-channel influence in an underwater acoustic multi-channel channel and reconstructing an acoustic pulse signal.

背景技术Background technique

脉冲信号是水声领域最常用的信号形式之一。受海底、海面及介质不均匀性的影响，海洋中的信号传播呈现多途特性，发射信号经过不同路径到达接收点，它们相互干涉叠加，导致接收点信号相对发射信号畸变严重，这为后续的信号检测、参数估计等信号处理带来很大困难。因此，采取有效措施实现抗信道多途是水声信号处理的关键技术之一。Pulse signal is one of the most commonly used signal forms in the field of underwater acoustics. Affected by the inhomogeneity of the seabed, sea surface and medium, the signal propagation in the ocean presents a multi-path characteristic. The transmitted signal arrives at the receiving point through different paths. Signal processing such as signal detection and parameter estimation brings great difficulties. Therefore, it is one of the key technologies of underwater acoustic signal processing to take effective measures to realize anti-channel multipath.

按照射线声学的理论，水声信道的输出可以等效为输入信号和信道单位冲激响应的时域卷积，因此水声多途信道可被看作一种卷积性干扰。同态滤波技术作为一种非线性信号处理技术，可将信号间的卷积关系转换成加性关系，再通过特征滤波器将两者分离，从而实现抗卷积干扰和信号重构的目的。According to the theory of ray acoustics, the output of the underwater acoustic channel can be equivalent to the time-domain convolution of the input signal and the unit impulse response of the channel, so the underwater acoustic multi-channel channel can be regarded as a kind of convolutional interference. Homomorphic filtering technology, as a nonlinear signal processing technology, can convert the convolution relationship between signals into an additive relationship, and then separate the two through feature filters, so as to achieve the purpose of anti-convolution interference and signal reconstruction.

在同态滤波过程中，特征滤波器的构建是一个非常重要的环节，也是影响信号重构（提纯）效果的关键所在，许多学者就此问题展开了研究。李爽（[1]同态滤波技术在水声信道中的应用.哈尔滨工程大学硕士学位论文.2010.：28-30页）提出可以采用线性滤波器将信道的倒谱分量滤除，获得直达声信号的倒谱，朱家兵（[2]倒谱技术的无源雷达直达波提纯方法.现代雷达.2007.8：75-78页）对现有的特征滤波方法进行了综合分析，包括低通滤波器和梳状滤波器。研究结果表明，低通滤波器会损失高时部分的信号复倒谱信息，因而重构误差较大；而梳状滤波器需要估计每条多途时延，构建条件严苛。因此，特征滤波构建仍然是同态滤波及信号重构技术的热点和难点问题。In the process of homomorphic filtering, the construction of feature filters is a very important link, and it is also the key to the effect of signal reconstruction (purification). Many scholars have conducted research on this issue. Li Shuang ([1] Application of Homomorphic Filtering Technology in Underwater Acoustic Channel. Master's Degree Thesis of Harbin Engineering University. 2010.: 28-30) proposed that a linear filter can be used to filter out the cepstrum component of the channel to obtain the direct acoustic The cepstrum of the signal, Zhu Jiabing ([2] Passive radar direct wave purification method of cepstrum technology. Modern Radar. 2007.8: 75-78) made a comprehensive analysis of the existing feature filtering methods, including low-pass filter and comb filter. The research results show that the low-pass filter will lose the complex cepstrum information of the high-time part of the signal, so the reconstruction error is relatively large; while the comb filter needs to estimate the time delay of each multi-path, and the construction conditions are strict. Therefore, feature filter construction is still a hot and difficult issue in homomorphic filtering and signal reconstruction technology.

发明内容Contents of the invention

本发明的目的在于提出一种构建简易、滤波效果良好的复倒谱域特征滤波方法,实现将信道输出信号中的多途信道分量滤除、重构激励源信号的目的。The purpose of the present invention is to propose a complex cepstrum domain feature filtering method with simple construction and good filtering effect, so as to achieve the purpose of filtering out multi-channel channel components in the channel output signal and reconstructing the excitation source signal.

本发明的目的是这样实现的：The purpose of the present invention is achieved like this:

(1)将信道输出信号经过卷积同态特征系统，将信号从时域转换到复倒谱域；(1) Pass the channel output signal through the convolution homomorphic feature system, and convert the signal from the time domain to the complex cepstrum domain;

(2)利用基于尖峰搜索思想构建复倒谱域滤波器并进行滤波，即根据信道的复倒谱特性，在复倒谱域上采用尖峰搜索的方法自动搜寻多途尖峰脉冲并对其进行平滑处理，从而实现复倒谱多途干扰的滤除；(2) Construct a complex cepstral domain filter based on the peak search idea and perform filtering, that is, according to the complex cepstral characteristics of the channel, use the peak search method in the complex cepstral domain to automatically search for multi-channel spikes and smooth them processing, so as to realize the filtering of complex cepstrum multi-path interference;

(3)将滤波后的结果经过卷积同态逆特征系统，实现声脉冲信号的重构。(3) The filtered result is passed through the convolution homomorphic inverse feature system to realize the reconstruction of the acoustic pulse signal.

所述利用基于尖峰搜索思想构建复倒谱域滤波器并进行滤波具体包括：The construction of a complex cepstral domain filter based on the idea of peak search and filtering specifically includes:

1）确定尖峰搜索的起始点n₀；1) Determine the starting point n₀ of peak search;

2）多途尖峰脉冲搜索，从起始点n₀开始逐点处理，通过能量判决及尖峰辨识组合策略完成多途尖峰脉冲的搜索；2) Multi-channel spike search, starting from the starting point n₀ to process point by point, and complete the search for multi-channel spikes through the combined strategy of energy judgment and peak identification;

3）多途尖峰脉冲滤除，对步骤2)中搜索到的多途尖峰脉冲做平滑处理，从而达到滤除多途影响的目的。3) Multi-channel spike filtering, smoothing the multi-channel spike pulses searched in step 2), so as to achieve the purpose of filtering out the influence of multiple channels.

本发明的核心技术内容在于基于尖峰搜索的复倒谱域滤波器构建及滤波，其基本思想是：在复倒谱域，信道多途的影响表现为在激励源信号的复倒谱中混入一系列的尖峰脉冲，据此本发明通过尖峰搜索的思想，将这些尖峰脉冲找到并予以滤除，以实现信道影响抑制的目的。The core technical content of the present invention lies in the construction and filtering of complex cepstrum domain filters based on peak search. A series of peak pulses, according to the idea of peak search in the present invention, these peak pulses are found and filtered, so as to achieve the purpose of channel impact suppression.

本发明的优点表现在：（1）本发明采用同态滤波思想进行多途信道抑制和信号重构，相对常用的自适应均衡、时间反转镜等技术而言，本发明无需预先知道信道或信号参数等先验知识，且适用于快变信道，对高速运动节点具有适应性。（2）本发明采用的基于尖峰搜索的复倒谱域特征滤波器构建，充分利用了复倒谱域信道多途的特点，采用尖峰干扰自动搜索的思想，只需预知信道的最小时延信息，构建方法简易、条件宽松。（3）本发明在复倒谱域滤波时对多途尖峰脉冲局部做平滑处理，尽可能的保留了信号复倒谱信息，使得滤波过程对信号影响细微，重构误差较小。The advantages of the present invention are as follows: (1) The present invention uses the idea of homomorphic filtering to suppress multi-channel channels and reconstruct signals. Compared with commonly used technologies such as adaptive equalization and time-reversal mirrors, the present invention does not need to know the channel or Prior knowledge such as signal parameters, and is suitable for fast-changing channels, and is adaptable to high-speed moving nodes. (2) The construction of the complex cepstrum domain feature filter based on peak search used in the present invention fully utilizes the multi-channel characteristics of the complex cepstrum domain channel, adopts the idea of automatic search for peak interference, and only needs to predict the minimum delay information of the channel , the construction method is simple and the conditions are loose. (3) The present invention performs local smoothing on the multi-path spikes during filtering in the complex cepstrum domain, and retains the complex cepstrum information of the signal as much as possible, so that the filtering process has a slight influence on the signal and the reconstruction error is small.

附图说明Description of drawings

图1(a)-图1(b)为发射声脉冲信号及其复倒谱波形图，其中：图1(a)为发射声脉冲信号时域波形，图1(b)为发射声脉冲信号复倒谱域波形。Figure 1(a)-Figure 1(b) are the transmitted acoustic pulse signal and its complex cepstrum waveform, where: Figure 1(a) is the time-domain waveform of the transmitted acoustic pulse signal, and Figure 1(b) is the transmitted acoustic pulse signal Complex Cepstral Domain Waveform.

图2(a)-图2(b)为信道冲激响应及其复倒谱波形图，其中：图2(a)为信道冲激响应时域波形，图2(b)为信道冲激响应复倒谱域波形。Figure 2(a)-Figure 2(b) are the channel impulse response and its complex cepstrum waveform, where: Figure 2(a) is the time-domain waveform of the channel impulse response, and Figure 2(b) is the channel impulse response Complex Cepstral Domain Waveform.

图3水声多途信道下声脉冲信号重构方法流程图。Fig. 3 is a flow chart of the acoustic pulse signal reconstruction method under the underwater acoustic multi-channel channel.

图4(a)-图4(b)为信道输出信号及其复倒谱图，其中：图4(a)为信道输出信号时域波形，图4(b)为信道输出信号复倒谱域波形。Figure 4(a)-Figure 4(b) is the channel output signal and its complex cepstrum diagram, wherein: Figure 4(a) is the time domain waveform of the channel output signal, and Figure 4(b) is the complex cepstrum domain of the channel output signal waveform.

图5(a)-图5(b)为基于尖峰搜索思想的复倒谱域滤波器构建及滤波效果图，其中：图5(a)为尖峰搜索法搜索到的多途尖峰脉冲，图5(b)为尖峰搜索法滤波后的复倒谱波形图。Figure 5(a)-Figure 5(b) are the complex cepstral domain filter construction and filtering effect diagram based on the peak search idea, in which: Figure 5(a) is the multi-channel spike searched by the peak search method, Figure 5 (b) is the complex cepstrum waveform filtered by the peak search method.

图6(a)-图6(b)为声脉冲信号重构结果及重构误差，其中：图6(a)为声脉冲信号重构结果，图6(b)为重构的声脉冲信号与发射声脉冲信号对比的误差。Figure 6(a)-Figure 6(b) is the reconstruction result and reconstruction error of the acoustic pulse signal, wherein: Figure 6(a) is the reconstruction result of the acoustic pulse signal, and Figure 6(b) is the reconstructed acoustic pulse signal The error compared to the transmitted acoustic pulse signal.

具体实施方式Detailed ways

下面结合附图和具体实施例对本发明作进一步具体说明：Below in conjunction with accompanying drawing and specific embodiment the present invention is described in further detail:

仿真条件：发射声脉冲信号为衰减指数加权的单频脉冲信号，中心频率1kHz，采样频率10kHz，信号长度0.2s。声源位置（0,0,100）m，接收机位置（50,50,50）m，海深200m。接收信号除直达声外，还有一次海底和海面反射声的叠加。图1为发射声脉冲号时域及复倒谱域波形图，图2为信道冲激响应时域及复倒谱域波形图。Simulation conditions: the transmitted sound pulse signal is a single-frequency pulse signal weighted by the attenuation index, the center frequency is 1kHz, the sampling frequency is 10kHz, and the signal length is 0.2s. Sound source position (0,0,100) m, receiver position (50,50,50) m, sea depth 200m. In addition to the direct sound, the received signal also has a superposition of the reflected sound from the seabed and the sea surface. Fig. 1 is the time domain and complex cepstral domain waveform diagram of the transmitted acoustic pulse signal, and Fig. 2 is the channel impulse response time domain and complex cepstrum domain waveform diagram.

本发明实现水声信道下声脉冲信号重构主要分为3个步骤，具体流程图详见图3。In the present invention, the reconstruction of the acoustic pulse signal under the underwater acoustic channel is mainly divided into three steps, and the specific flow chart is shown in FIG. 3 .

1.将信道输出信号经过卷积同态特征系统，将信号从时域转换到复倒谱域。1. Pass the channel output signal through the convolution homomorphic feature system, and convert the signal from the time domain to the complex cepstrum domain.

所谓同态滤波的特征系统，就是对信道输出信号x(n)做复倒谱变换，即：The so-called characteristic system of homomorphic filtering is to perform complex cepstrum transformation on the channel output signal x(n), namely:

$\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>F</span>f</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>[</span>[</span>\mathrm{<span><span>ln</span>ln</span>}<span><span>(</span>(</span>\mathrm{<span><span>X</span>x</span>}<span><span>(</span>(</span>{\mathrm{<span><span>e</span>e</span>}}^{\mathrm{<span><span>j\&omega;</span>j\&omega;</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

其中，是x(n)的复倒谱，信号X(e^jω)是x(n)的傅立叶变换，F^-1[□]代表傅立叶反变换。in, is the complex cepstrum of x(n), the signal X(e^jω ) is the Fourier transform of x(n), and F^-1 [□] represents the inverse Fourier transform.

经过式（1）所示的变换过程，信道输出信号从时域变换到复倒谱域，同时发射信号和信道干扰从时域的卷积关系转换为复倒谱域的加性关系，结果如图4所示。After the transformation process shown in formula (1), the channel output signal is transformed from the time domain to the complex cepstrum domain, and the transmitted signal and channel interference are converted from the convolutional relationship in the time domain to the additive relationship in the complex cepstral domain. The result is as follows Figure 4 shows.

2.基于尖峰搜索思想构建复倒谱域滤波器并进行滤波，即根据信道的复倒谱特性，在复倒谱域上采用尖峰搜索的方法自动搜寻多途尖峰脉冲并对其进行平滑处理，从而实现复倒谱多途干扰的滤除。2. Construct a complex cepstrum domain filter based on the peak search idea and perform filtering, that is, according to the complex cepstrum characteristics of the channel, use the peak search method in the complex cepstrum domain to automatically search for multi-path peaks and smooth them, In this way, the filtering of complex cepstrum multi-path interference is realized.

设h(n)为水声信道冲激序列：Let h(n) be the impulse sequence of the underwater acoustic channel:

$\mathrm{<span><span>h</span>h</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

式中，a_i和n_i分别是声波沿第i条路径到达接收点的信号声压幅度和时延量,N为路径数。In the formula, a_i and_ni are respectively the signal sound pressure amplitude and time delay of the sound wave arriving at the receiving point along the i-th path, and N is the number of paths.

经推导，该水声信道冲激序列在复倒谱域主要由以下三部分组成：After derivation, the underwater acoustic channel impulse sequence mainly consists of the following three parts in the complex cepstrum domain:

第一部分：first part:

$\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>+</span>+</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>+</span>+</span>\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>N</span>N</span>}}}{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>N</span>N</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

第二部分：the second part:

$\begin{array}{c}<span><span>-</span>-</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>\mathrm{<span><span>2</span>2</span>}<span><span>(</span>(</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>-</span>-</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>-</span>-</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>2</span>2</span>}}{<span><span>(</span>(</span>\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>N</span>N</span>}}}{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>\mathrm{<span><span>2</span>2</span>}<span><span>(</span>(</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>N</span>N</span>}}<span><span>)</span>)</span><span><span>)</span>)</span>\\ <span><span>-</span>-</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>j</span>j</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>j</span>j</span>}}}{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>2</span>2</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

第三部分：the third part:

$\begin{array}{c}\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>2</span>2</span>}}^{\mathrm{<span><span>3</span>3</span>}}}{{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>3</span>3</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>3</span>3</span>}}<span><span>)</span>)</span><span><span>+</span>+</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span>\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>N</span>N</span>}}^{\mathrm{<span><span>3</span>3</span>}}}{{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>3</span>3</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>N</span>N</span>}}<span><span>)</span>)</span><span><span>+</span>+</span>\frac{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>3</span>3</span>}}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>j</span>j</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>j</span>j</span>}}}{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>3</span>3</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>\\ <span><span>+</span>+</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>z</span>z</span>}<span><span>=</span>=</span>\mathrm{<span><span>2</span>2</span>}<span><span>,</span>,</span>\mathrm{<span><span>i</span>i</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>j</span>j</span>}<span><span>\&NotEqual;</span>\&NotEqual;</span>\mathrm{<span><span>z</span>z</span>}}{\overset{\mathrm{<span><span>N</span>N</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>j</span>j</span>}}{\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>z</span>z</span>}}}{{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>a</span>a</span>}}_{\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>3</span>3</span>}}}\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>+</span>+</span>{\mathrm{<span><span>3</span>3</span>}\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>n</span>no</span>}}_{\mathrm{<span><span>z</span>z</span>}}<span><span>)</span>)</span>\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

可见，水声信道冲激序列经过复倒谱变换后仍然是一个冲激序列，只是序列延拓变为无限长；原序列上的每一个多途尖峰脉冲都会以其相对于直达波延迟时间进行周期延拓，同时每条多途尖峰时延的加性组合处也会出现尖峰；尖峰幅度随时间的增大而衰减，且衰减速度比原序列更快。It can be seen that the impulse sequence of the underwater acoustic channel is still an impulse sequence after complex cepstrum transformation, but the sequence continuation becomes infinitely long; The period is extended, and at the same time, a peak will appear at the additive combination of each multi-path peak delay; the peak amplitude decays with time, and the decay speed is faster than the original sequence.

根据上述声信道的复倒谱特性，在复倒谱域上采用尖峰搜索和平滑处理的方法进行滤波。具体步骤如下：According to the complex cepstrum characteristics of the above-mentioned acoustic channel, the method of peak search and smoothing is used for filtering in the complex cepstrum domain. Specific steps are as follows:

(1)确定起始点n₀。将输出信号复倒谱上的第一个尖峰作为信道最小时延，然后将搜索的起始点设置在该时延右侧。以本仿真条件为例，起始点n₀=210。(1) Determine the starting point n₀ . The first peak on the complex cepstrum of the output signal is taken as the minimum channel delay, and then the starting point of the search is set on the right side of the delay. Taking this simulation condition as an example, the starting point n₀ =210.

(2)多途尖峰脉冲搜索。从起始点开始逐一处理，通过能量判决及尖峰辨识组合策略完成多途尖峰脉冲的搜索，即判定点n为多途尖峰脉冲需满足两个条件：(2) Multi-channel spike search. Start from the starting point to process one by one, and complete the search for multi-channel spikes through the combined strategy of energy judgment and peak identification, that is, the decision point n is a multi-channel spike that needs to meet two conditions:

1)能量判决。设置幅度值门限β=0.02，点n的幅度需大于此门限值，以避免误判零1) Energy judgment. Set the amplitude value threshold β=0.02, and the amplitude of point n must be greater than this threshold value to avoid misjudgment of zero

值周围的点为多途尖峰脉冲。The dots around the value are multipath spikes.

2)尖峰辨识。对于满足条件1)的点，该点的幅度需比周围点的幅度高出一定量级，即设一个正数M=0.6|n|，点n与点n-1幅度绝对值的需差大于M，同时n与n+1幅度的绝对值的差也需大于M。其中，M值的选取需视实际情况而定，M值太高会漏判峰值，使重构出的信号有偏差，M值太低会造成误判，损失信号能量。2) Peak identification. For a point that satisfies condition 1), the amplitude of this point must be higher than the amplitude of the surrounding points by a certain order, that is, a positive number M=0.6|n| is set, and the difference between the absolute value of the amplitude of point n and point n-1 needs to be greater than M, and the difference between the absolute value of the amplitude of n and n+1 must also be greater than M. Among them, the selection of the M value depends on the actual situation. If the M value is too high, the peak value will be missed and the reconstructed signal will be biased. If the M value is too low, it will cause misjudgment and loss of signal energy.

(3)多途尖峰脉冲滤除。确定某点n为多途尖峰脉冲后，采用中值平滑的思想将其滤除，即将点n的幅值替换为点n-1与n+1点幅值的均值。(3) Multi-channel peak pulse filtering. After determining that a certain point n is a multi-channel spike, it is filtered out by using the idea of median smoothing, that is, the amplitude of point n is replaced by the average value of the amplitudes of point n-1 and point n+1.

基于尖峰搜索思想的复倒谱域滤波器构建及滤波效果图如图5所示。The complex cepstral domain filter construction and filtering effect diagram based on the peak search idea are shown in Figure 5.

3.将滤波后的结果经过卷积同态逆特征系统，实现声脉冲信号的重构。3. Pass the filtered result through the convolution homomorphic inverse feature system to realize the reconstruction of the acoustic pulse signal.

所谓卷积同态逆特征系统，就是对滤波后的复倒谱结果做逆复倒谱变换，获得重构的声脉冲信号x'(n)，即：The so-called convolution homomorphic inverse feature system is to perform inverse complex cepstrum transformation on the filtered complex cepstrum result to obtain the reconstructed acoustic pulse signal x'(n), namely:

${\mathrm{<span><span>x</span>x</span>}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>F</span>f</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>[</span>[</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span>{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>x</span>x</span>}}}^{<span><span>\&prime;</span>\&prime;</span>}<span><span>(</span>(</span>\mathrm{<span><span>n</span>no</span>}<span><span>)</span>)</span><span><span>)</span>)</span><span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

其中，是经步骤2获得的滤除多途尖峰脉冲后的复倒谱结果，exp(·)代表指数运算，F^-1[□]代表傅立叶反变换。重构出的声脉冲信号及重构误差如图6所示。in, is the complex cepstrum result obtained in step 2 after filtering multi-channel spikes, exp(·) represents exponential operation, and F^-1 [□] represents inverse Fourier transform. The reconstructed acoustic pulse signal and the reconstruction error are shown in Figure 6.

最后应说明的是，以上实施例仅用以描述本发明的技术方案而不是对本技术方法进行限制，本发明在应用上可以延伸为其他的修改、变化、应用和实施例，并且因此认为所有这样的修改、变化、应用、实施例都在本发明的精神和教导范围内。Finally, it should be noted that the above embodiments are only used to describe the technical solutions of the present invention rather than limit the technical methods of the present invention. The present invention can be extended to other modifications, changes, applications and embodiments in application, and therefore it is considered that all such Modifications, changes, applications, and embodiments are all within the spirit and teaching scope of the present invention.

Claims (1)

1. A method for reconstructing an acoustic pulse signal under an underwater acoustic multi-path channel is characterized by comprising the following steps:

(1) the channel output signal is converted into a complex cepstrum domain from a time domain through a convolution homomorphic characteristic system; the convolution homomorphic feature system performs complex cepstrum transformation on a channel output signal x (n), namely:

$\hat{x}\left(n\right)=F^{-1}\left[\ln \left(X\left(e^j\right)\right)\right]$

wherein,is a complex cepstrum of X (n), signal X (e)^jω) Is the Fourier transform of x (n), F^-1[·]Represents an inverse fourier transform;

(2) the method comprises the following steps of constructing a complex cepstrum domain filter based on a peak searching idea and filtering, namely automatically searching multipath peak pulses on a complex cepstrum domain by adopting a peak searching method according to the complex cepstrum characteristics of a channel and smoothing the multipath peak pulses, thereby filtering multipath interference of the complex cepstrum, and specifically comprises the following steps:

(2.1) determining a starting point n of the spike search₀；

(2.2) multipath spike search from the starting point n₀Starting point-by-point processing, and completing the search of multi-path spike pulses through an energy judgment and spike identification combined strategy; namely, the decision point n is the multi-path spike pulse and needs to satisfy two conditions:

(A) energy judgment, namely setting an amplitude value threshold beta to be 0.02, wherein the amplitude of a point n is larger than the threshold;

(B) identifying a peak, namely, for a point meeting the condition (A), the amplitude of the point is higher than the amplitude of surrounding points by a certain magnitude, namely, a positive number M is set to be 0.6| n |, the difference between the absolute value of the amplitude of the point n and the absolute value of the amplitude of the point n-1 is larger than M, and the difference between the absolute value of the amplitude of n and the absolute value of the amplitude of n +1 is also larger than M;

(2.3) filtering the multi-path spike pulse, and smoothing the multi-path spike pulse searched in the step 2), thereby achieving the purpose of filtering the multi-path influence;

(3) the filtered result is processed by a convolution homomorphic inverse characteristic system to realize the reconstruction of the acoustic pulse signal; the convolution homomorphic inverse characteristic system performs inverse complex cepstrum transformation on the filtered complex cepstrum result to obtain a reconstructed acoustic pulse signal x' (n), namely:

<math> <mrow> <msup> <mi>x</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>F</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>[</mo> <mi>exp</mi> <mrow> <mo>(</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>]</mo> </mrow></math>

wherein,is the complex cepstrum result after the filtering of the complex cepstrum multipath interference realized by the step (2), exp (-) represents the exponential operation, F^-1[·]Representing the inverse fourier transform.