Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

A novel internet traffic identification approach using wavelet packet decomposition and neural network

Internet traffic classification plays an important role in network management, and many approaches have been proposed to classify different kinds of internet traffics. A novel approach was proposed to classify network applications by optimized back-propagation (BP) neural network. Particle swarm optimization (PSO) algorithm was used to optimize the BP neural network. And in order to increase the identification performance, wavelet packet decomposition (WPD) was used to extract several hidden features from the time-frequency information of network traffic. The experimental results show that the average classification accuracy of various network applications can reach 97%. Moreover, this approach optimized by BP neural network takes 50% of the training time compared with the traditional neural network.

Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

One of the important issues in the system identification and the spectrum analysis is the frequency resolution, i.e., the capability of distinguishing between two or more closely spaced frequency components. In the modal identification by the empirical mode decomposition （EMD） method, because of the separating capability of the method, it is still a challenge to consistently and reliably identify the parameters of structures of which modes are not well separated. A new method is introduced to generate the intrin- sic mode functions （IMFs） through the filtering algorithm based on the wavelet packet decomposition （GIFWPD）. In this paper, it is demonstrated that the CIFWPD method alone has a good capability of separating close modes, even under the severe condition beyond the critical frequency ratio limit which makes it impossible to separate two closely spaced harmonics by the EMD method. However, the GIFWPD-only based method is impelled to use a very fine sampling frequency with consequent prohibitive computational costs. Therefore, in order to decrease the computational load by reducing the amount of samples and improve the effectiveness of separation by increasing the frequency ratio, the present paper uses a combination of the complex envelope displacement analysis （CEDA） and the GIFWPD method. For the validation, two examples from the previous works are taken to show the results obtained by the GIFWPD-only based method and by combining the CEDA with the GIFWPD method.

Time Domain Signal Analysis Using Wavelet Packet Decomposition Approach

This paper explains a study conducted based on wavelet packet transform techniques. In this paper the key idea underlying the construction of wavelet packet analysis (WPA) with various wavelet basis sets is elaborated. Since wavelet packet decomposition can provide more precise frequency resolution than wavelet decomposition the implementation of one dimensional wavelet packet transform and their usefulness in time signal analysis and synthesis is illustrated. A mother or basis wavelet is first chosen for five wavelet filter families such as Haar, Daubechies (Db4), Coiflet, Symlet and dmey. The signal is then decomposed to a set of scaled and translated versions of the mother wavelet also known as time and frequency parameters. Analysis and synthesis of the time signal is performed around 8 seconds to 25 seconds. This was conducted to determine the effect of the choice of mother wavelet on the time signals. Results are also prepared for the comparison of the signal at each decomposition level. The physical changes that are occurred during each decomposition level can be observed from the results. The results show that wavelet filter with WPA are useful for analysis and synthesis purpose. In terms of signal quality and the time required for the analysis and synthesis, the Haar wavelet has been seen to be the best mother wavelet. This is taken from the analysis of the signal to noise ratio (SNR) value which is around 300 dB to 315 dB for the four decomposition levels.

Features of energy distribution for blast vibration signals based on wavelet packet decomposition

Blast vibration analysis constitutes the foundation for studying the control of blasting vibration damage and provides the precondition of controlling blasting vibration. Based on the characteristics of short-time nonstationary random signal, the laws of energy distribution are investigated for blasting vibration signals in different blasting conditions by means of the wavelet packet analysis technique. The characteristics of wavelet transform and wavelet packet analysis are introduced. Then, blasting vibration signals of different blasting conditions are analysed by the wavelet packet analysis technique using MATLAB; energy distribution for different frequency bands is obtained. It is concluded that the energy distribution of blasting vibration signals varies with maximum decking charge,millisecond delay time and distances between explosion and the measuring point. The results show that the wavelet packet analysis method is an effective means for studying blasting seismic effect in its entirety, especially for constituting velocity-frequency criteria.

Adaptive Bearing Fault Diagnosis based on Wavelet Packet Decomposition and LMD Permutation Entropy

Bearing fault signal is nonlinear and non-stationary, therefore proposed a fault feature extraction method based on wavelet packet decomposition （WPD） and local mean decomposition （LMD） permutation entropy, which is based on the support vector machine （SVM） as the feature vector pattern recognition device Firstly, the wavelet packet analysis method is used to denoise the original vibration signal, and the frequency band division and signal reconstruction are carried out according to the characteristic frequency. Then the decomposition of the reconstructed signal is decomposed into a number of product functions （PE） by the local mean decomposition （LMD） , and the permutation entropy of the PF component which contains the main fault information is calculated to realize the feature quantization of the PF component. Finally, the entropy feature vector input multi-classification SVM, which is used to determine the type of fault and fault degree of bearing The experimental results show that the recognition rate of rolling bearing fault diagnosis is 95%. Comparing with other methods, the present this method can effectively extract the features of bearing fault and has a higher recognition accuracy

Wavelet packet decomposition entropy threshold method for discrete spectrum interferences rejection of on-line partial discharge monitoring

The frequency domain division theory of dyadic wavelet decomposition and wavelet packet decomposition (WPD) with orthogonal wavelet base frame are presented. The WPD coefficients of signals are treated as the outputs of equivalent bandwidth filters with different center frequency. The corresponding WPD entropy values of coefficients increase sharply when the discrete spectrum interferences (DSIs), frequency spectrum of which is centered at several frequency points existing in some frequency region. Based on WPD, an entropy threshold method (ETM) is put forward, in which entropy is used to determine whether partial discharge (PD) signals are interfered by DSIs. Simulation and real data processing demonstrate that ETM works with good efficiency, without pre-knowing DSI information. ETM extracts the phase of PD pulses accurately and can calibrate the quantity of single type discharge.

数控机床电动主轴WPD-TSNE-SVM模型故障诊断

为了提高数控机床电动主轴故障诊断效率,设计了一种WPD-TSNE-SVM组合模型。利用小波包方法分解主轴振动信号,并完成样本集TSNE降维的过程,利用SVM完成重构特征的故障分类。构建数控机床主轴信号混合特征空间向量,并进行故障诊断分析。研究结果表明:TSNE方法训练样数据形成规律分布特点,采用非线性SVM多故障分类器实现小波包混合特征的故障准确分类。根据径向基核函数建立的非线性SVM诊断方法获得更高准确率。该方法诊断轴承运行故障,获得更高维护效率,确保数控机床主轴运行稳定性。

基于WPD-ARIMA-GARCH组合模型的酱卤肉制品安全风险区间预测

针对传统确定性预测不能提供不确定性信息的难题,本研究提出了一种点估计和区间估计组合预测模型,并将其创新性地应用在食品安全风险预警领域。在点估计部分,使用小波包分解(wavelet packet decomposition,WPD)对周风险等级序列分解后,应用差分自回归移动平均(autoregressive integrated moving average,ARIMA)模型进行预测;在区间估计部分,使用广义自回归条件异方差(generalized autoregressive conditional heteroskedast,GARCH)模型对残差进行预测。本实验将建立的WPD-ARIMA-GARCH组合模型运用于某地区酱卤肉制品的风险预测,结果表明2019年的3月底和7月底该地区的酱卤肉制品安全风险较高,与实际情况相符;同时,该模型在10个不同地区的酱卤肉制品风险预测中,均方误差、平均绝对误差和平均绝对百分比误差分别为1.626、0.806和20.824;其90%置信区间的预测区间平均宽度和覆盖宽度标准值均为0.024,可以覆盖所有真实值。该模型具有较高的预测精度和较低的误差,能对酱卤肉制品质量安全起到风险防控作用,可为日常食品安全监管提供相应的技术支持。

Application and improvement of wavelet packet de-noising in satellite transponder

The satellite transponder is a widely used module in satellite missions, and the most concerned issue is to reduce the noise of the transferred signal. Otherwise, the telemetry signal will be polluted by the noise contained in the transferred signal, and the additional power will be consumed. Therefore, a method based on wavelet packet de-noising （WPD） is introduced. Compared with other techniques, there are two features making WPD more suit- able to be applied to satellite transponders： one is the capability to deal with time-varying signals without any priori information of the input signals; the other is the capability to reduce the noise in band, even if the noise overlaps with signals in the frequency domain, which provides a great de-noising performance especially for wideband signals. Besides, an oscillation detector and an av- eraging filter are added to decrease the partial oscillation caused by the thresholding process of WPD. Simulation results show that the proposed algorithm can reduce more noises and make less distortions of the signals than other techniques. In addition, up to 12 dB additional power consumption can be reduced at -10 dB signal-to-noise ratio （SNR）.

Distance Measuring Equipment Pulse Interference Suppression Based on Wavelet Packet Analysis

As an indispensable part of global satellite navigation system, the frequency band of DME will overlap with that of the navigation signal, which will cause the signal from the DME platform to be accepted by the Global Navigation Satellite System receiver and form interference. Therefore, it is of great significance to study an effective algorithm to suppress DME pulse interference. This paper has the following research on this problem. In this paper, wavelet packet transform is used to solve for the suppression of DME pulse interference method, wavelet packet analysis belongs to the linear time-frequency analysis method, it has good time-frequency localization characteristics and the signal adaptive ability, due to the function of wavelet packet and parameter selection of DME will affect the ability of interference suppression, combining with the theory of wavelet threshold, function type and decomposition series are discussed to prove the validity of the selected parameters on the pulse interference suppression.

基于WPD-EMD-WPD的地下工程微震信号降噪方法研究

微震信号中的背景噪声会影响初至拾取、震源定位及参数反演,合理有效的降噪方法是微震监测技术成功应用于工程建设的重要基础。本文提出一种基于WPD-EMD-WPD的方法抑制噪声,并采用信偏比衡量降噪效果。该方法首先对含噪信号小波包预降噪,实现初次滤波;然后对预降噪后的信号进行经验模态分解(Empirical Mode Decomposition,EMD),自适应分解得到IMFS,通过相关系数法确定IMFS分解分量位置;最后,对分界分量之前的高频分量小波包降噪,再与低频分量重构。分别使用小波包、EMD、EMD-WPD、WPD-EMD-WPD 4种方法进行仿真实验,对含噪Ricker子波降噪处理,通过对比降噪前后的降噪效果衡量指标、频谱图、波形图对比发现,WPD-EMD-WPD降噪效果更优,且信偏比与其他降噪指标有良好对应性。将该方法应用于国内某大型水电工程地下洞室,结果表明,该方法能获得更低的信偏比,且能更好地反映初至时刻和岩石微破裂信息。

基于WPD的光缆中间接头局部光纤通信信号去噪技术研究

光缆运行工作过程中,由于光缆质地较脆,抗机械摩擦强度较差,光缆中间接头部分易产生局部的通信信号噪声干扰。为此,设计基于小波包分解(WPD)的光缆中间接头局部光纤通信信号去噪方法。从白噪声和窄带噪声2个方面,结合损伤区域提取损伤后的局部噪声干扰特性,设置WPD算法的去噪阈值。以分层去噪的方式得出局部光纤通信信号去噪结果。实验结果表明,在不同的损伤干扰强度条件下,所提方法得出光纤通信信号的信噪比较高,去噪效果好。

基于PCA-WPD优化的电流互感器故障检测方法研究

针对电磁式电流互感器测量误差的长期稳定性较差问题,提出主成分分析小波包分解的电流互感器故障测量误差自检测方法。利用小波包分解优化残差统计量,可以消除电流互感器设备中节点不平衡和随机误差对检测分析结果的影响。实验结果表明,随着测量误差的增加,测量数据的残差统计量逐渐增加。所提出的电流互感器故障检测方法能较好地满足0.2级精度的要求,且可以检测到电流互感器异常数据占90.97%,占总数的53.17%。该方法能够及时准确地实现电流互感器故障测量误差的自检测。

脑机接口中基于WPD和CSP的特征提取

针对脑机接口(brain computer interface,BCI)中2类运动想象任务的特征提取问题,提出了一种小波包分解(wavelet packet decomposition,WPD)与共同空间模式(common spatial pattern,CSP)相结合的脑电信号特征提取方法。该方法首先选择7个重要导联的脑电(electroencephalograph,EEG)信号,用‘haar’小波基进行三阶WPD分解;然后对每个导联分解后的其中5个子带进行重构,获取相关频域信息;最后对重构后信号利用CSP特征提取,获得六维特征向量。CSP与WPD相结合能够充分利用WPD的时频特性,有效避免CSP要求输入导联数过多、缺乏频域信息等缺陷。对2008年国际BCI竞赛数据和本实验室实验数据,采用该方法进行特征提取,通过概率神经网络(probabilistic neural network,PNN)分类。2种数据源分类正确率分别为92%和80%,相对于单纯的CSP特征提取,正确率分别提高5%和20%。实验结果表明:WPD与CSP相结合的特征提取算法能提取明显的特征,进而提高BCI的识别正确率。

基于声发射信号EMD-WPD特征融合的航天器在轨泄漏辨识方法

长期运行在空间环境中的航天器可能由于撞击、振动、老化等因素而发生气体泄漏,在轨泄漏辨识对航天器安全保障具有重要意义。提出了一种基于声发射信号经验模态分解(empirical mode decomposition,EMD)和小波包分解(wavelet packet decomposition,WPD)特征融合的航天器泄漏辨识方法,首先将声发射信号分别通过EMD和WPD分解成为不同频率范围内的子带信号,考虑能量特征误差与不稳定性,提取信号无量纲因子和频率特征参数并应用Relief F算法选取特征。最后,构建支持向量机(support vector machines,SVM)机器学习数据库,训练泄漏分类模型并利用测试集交叉验证模型分类精度。结果表明,EMD和WPD分解特征并行融合分类模型可显著提高辨识精度,最高可达96.9%,且输入特征数量少,是一种具有应用前景的航天器在轨气体泄漏辨识方法。

基于WPD-CNN二维时频图像的滚动轴承故障诊断

滚动轴承故障诊断是现代工业发展中的重要技术。针对滚动轴承信号特征提取与智能诊断问题,提出了一种基于WPD-CNN二维时频图像的滚动轴承故障诊断方法。首先通过小波包分解(WPD)将信号转换为二维时频图像;其次将时频图像输入VGG19卷积神经网络(CNN)模型自动提取有效特征,并输入Softmax分类器进行训练;最后使用训练好的分类器完成滚动轴承故障诊断任务。实验结果表明,10类故障数据的识别准确率均在98.3%左右,高于其他深度学习和传统方法,因此所提出的故障诊断模型能有效地进行滚动轴承复杂信号的特征提取以及分类任务。

基于WPD和（2D）~2PCA的步态识别方法

为了提高步态识别率,在步态能量图(gait energy image,GEI)基础上,提出了基于小波包分解(waveletpacket decomposition,WPD)和完全主成分分析(two-directional two-dimensional principal component analysis,(2D)2PCA)的步态识别方法.该方法采用基于人体轮廓的GEI来解决步态数据量过大的问题,并采用WPD和(2D)2PCA进行步态特征提取,解决了已有基于小波变换的步态识别方法中高频分量丢失或维数过高问题.在NLPR步态数据库上对该方法进行了评测,并与经典方法进行了比较.实验结果表明:该方法具有更高的识别率和视角变化的鲁棒性.

基于WPD和EMD的噪声品质预测模型

声品质作为汽车舒适性的一个重要指标,目前已经成为汽车领域一个重要的研究方向。根据人耳的听觉特性,提出一种基于小波包分解(WPD)和经验模态分解(EMD)的21个特征频带划分方法。按照所提出的方法,将采集得到的车辆噪声信号进行分解并提取信号在各频带的声能量时变特征。之后根据BP神经网络原理将提取的能量特征作为输入,计算得出响度和尖锐度等声品质评价参数作为输出,建立一种基于WPD和EMD的声品质评价模型。验证结果表明,所建立的模型可以准确地预测响度和尖锐度等心理声学参数,可作为声品质评价的一种有效方法。