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.

The Time-frequency Characteristic of a Large Volume Airgun Source Wavelet and Its Influencing Factors

Through analyzing the near-field hydrophone records of the airgun experiment in the Jiemian reservoir,Fujian,we study the time-frequency characteristic of airgun source wavelet and the influence of gun depth and firing pressure,and explain the process of bubble oscillation based on the Johnson( 1994) bubble model. The data analysis shows that:( 1) Airgun wavelet is composed of primary pulse and bubble pulse. The primary pulse,which is of large amplitude,short duration and wide frequency band,is usually used in shallow exploration. The bubble pulse,which is concentrated in the low-frequency range,is usually used in deep exploration with deep vertical penetration and far horizontal propagation.( 2) The variation of primary pulse amplitude with gun depth is very small,bubble pulse amplitude and the dominant frequency increase,and peak-bubble ratio and bubble period decrease. When the gun depth is 10 m,primary pulse amplitude and peakbubble ratio are maximum,which is suitable for shallow exploration; when gun depth is25 m,bubble pulse amplitude is large, and peak-bubble ratio is minimum, which is suitable for deep exploration.( 3) The primary pulse amplitude,bubble pulse amplitude,peak-bubble ratio,and bubble period increase and the dominant frequency decreases with increased firing pressure.

Application of Wavelet Packet De-noising in Time-Frequency Analysis of the Local Wave Method

The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.

Improving the resolution of seismic traces based on the secondary time-frequency spectrum

The resolution of seismic data is critical to seismic data processing and the subsequent interpretation of fine structures. In conventional resolution improvement methods, the seismic data is assumed stationary and the noise level not changes with space, whereas the actual situation does not satisfy this assumption, so that results after resolution improvement processing is not up to the expected effect. To solve these problems, we propose a seismic resolution improvement method based on the secondary time-frequency spectrum. First, we propose the secondary time-frequency spectrum based on S transform （ST） and discuss the reflection coefficient sequence and time-dependent wavelet in the secondary time frequency spectrum. Second, using the secondary time frequency spectrum, we design a two- dimensional filter to extract the amplitude spectrum of the time-dependent wavelet. Then, we discuss the improvement of the resolution operator in noisy environments and propose a novel approach for determining the broad frequency range of the resolution operator in the time- fi＇equency-space domain. Finally, we apply the proposed method to synthetic and real data and compare the results of the traditional spectrum-modeling deconvolution and Q compensation method. The results suggest that the proposed method does not need to estimate the Q value and the resolution is not limited by the bandwidth of the source. Thus, the resolution of the seismic data is improved sufficiently based on the signal-to-noise ratio （SNR）.

Phase estimation in bispectral domain based on conformal mapping and applications in seismic wavelet estimation

Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. Wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.

Time-Frequency Analysis of EEG Signals Evoked by Voluntary, Stimulated and Imaginary Motions

In order to investigate the characteristics of sensorimotor cortex during motor execution(ME), voluntary, stimulated and imaginary finger flexions were performed by ten volunteer subjects. Electroencephalogram(EEG) data were recorded according to the modified 10-20 International EEG System. The patterns were compared by the analysis of the motion-evoked EEG signals focusing on the contralateral(C3) and ipsilateral(C4) channels for hemispheric differences. The EEG energy distributions at alpha(8—13 Hz), beta(14—30 Hz) and gamma(30—50 Hz) bands were computed by wavelet transform(WT) and compared by the analysis of variance(ANOVA). The timefrequency(TF) analysis indicated that there existed a contralateral dominance of alpha post-movement event-related synchronization(ERS) pattern during the voluntary task, and that the energy of alpha band increased in the ipsilateral area during the stimulated(median nerve of wrist) task. Besides, the contralateral alpha and beta event-related desynchronization(ERD) patterns were observed in both stimulated and imaginary tasks. Another significant difference was found in the mean power values of gamma band(p<0.01)between the imaginary and other tasks. The results show that significant hemispheric differences such as alpha and beta band EEG energy distributions and TF changing phenomena(ERS/ERD) were found between C3 and C4 areas during all of the three patterns. The largest energy distribution was always at the alpha band for each task.

A novel image fusion algorithm based on 2D scale-mixing complex wavelet transform and Bayesian MAP estimation for multimodal medical images

In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.

Novel Time-frequency Analysis and Representation of EEG

A novel method of EEG time-frequency analysis and representation based on a wavelet network is presented. The wavelet network model can represent the EEG data effectively. Based on the wavelet network model, a novel time-frequency energy distribution function is obtained, which has the same time-frequency resolution as Wigner-Ville distribution and is free of cross-term interference. There is a great potential for the use of the novel time-frequency representation of nonstationary biosignal based on a wavelet network in the field of the electrophysiological signal processing and time-frequency analysis.

基于特征图像组合与改进ResNet-18的电能质量扰动识别方法

针对传统电能质量扰动(power quality disturbance,PQD)识别体系中单一图像特征信息受限与算法识别能力不足等问题,依据特征融合的思想,提出一种基于特征图像组合与改进ResNet-18的PQD识别方法。首先,对PQD信号进行变分模态分解(variational mode decomposition,VMD)得到一系列固有模态函数(intrinsic mode functions,IMFs)与残差分量;其次,将IMFs、残差分量、原始扰动信号与Subtract分量纵向拼接成分量矩阵,利用信号-图像转化方法生成特征分量彩色图;再次,对原始扰动信号进行连续小波变换(continuous wavelet transform,CWT)生成小波时-频图;最后,将特征分量彩色图与小波时-频图组合输入改进的六通道ResNet-18中训练学习并完成扰动识别。通过仿真对PQD识别方法进行分析并将其与目前常用识别体系进行比较。结果表明,所提方法具有较好的抗噪性能并且能够更好地提取PQD特征信息,达到更高的识别准确率。

基于改进ResNet50的表面肌电信号手势识别

为了提高手势动作在类别众多且相似度高的情况下的识别精度,提出了一种基于连续小波变换和残差神经网络Res-Net50的表面肌电信号手势识别方法。首先对Ninapro DB2和DB3的原始表面肌电信号进行预处理和连续小波变换,得到Multi-sEMG Wavelet Map数据集,然后送入改进的ResNet50模型进行识别分类。实验结果表明,改进后的ResNet50网络模型在Multi-sEMG Wavelet Map DB2和DB3中17种手势动作的平均准确率分别达到了96.40%和94.11%,相比ResNet50网络模型方法提升了4.87%和5.83%。实现了手势动作在类别繁多、相似度较高的情况下的精准识别。为基于非侵入式传感器和机器学习控制的假肢手提供了新方案。

融合T-分布小波变异的混沌鲸鱼优化算法

针对鲸鱼优化算法难以跳出局部最优导致收敛精度不足的问题,提出一种融合了T-分布小波变异和多项式差分学习策略的鲸鱼优化算法.该算法首先引入Circle混沌扩大搜索范围,提高收敛速度;然后采用T-分布小波变异策略平衡全局和局部搜索能力;最后采用多项式差分学习策略改进算法的优化精度.对3种改进策略作单一引入的仿真对比分析,并将改进的鲸鱼优化算法在12个可变维度的基准测试函数上进行仿真,对本文改进的鲸鱼优化算法与其他改进策略的鲸鱼优化算法以及其他几种智能算法进行比较.结果表明,基于T-分布小波变异和多项式差分学习策略的改进鲸鱼优化算法具有较好的稳定性,收敛速度和精度更好.

基于MDS和改进SSA-SVM的高速铁路道岔故障诊断方法研究

针对高速铁路道岔设备故障频繁,现场维修工作量大等问题,提出基于多维尺度缩放法(MDS)和改进麻雀搜索算法(SSA)优化支持向量机(SVM)的高速铁路道岔故障诊断模型。首先以ZDJ9道岔转换功率曲线为研究对象,总结现场典型道岔故障类型及故障原因,分别提取道岔功率曲线的时域、频域特征指标以及小波包能量熵,组成特征指标向量;其次采用MDS方法进行多维特征指标的降维优化,建立道岔故障特征指标样本数据库;最后利用改进Circle混沌映射初始化种群,并通过自适应t分布增强麻雀种群的多样性,再以改进SSA算法优化SVM模型中的惩罚因子和核函数方差2个关键参数,构建改进SSA-SVM的道岔故障诊断模型。故障诊断结果表明,本模型的故障诊断正确率高达96.25%,诊断效果优于其他方法,可以为道岔设备的故障维修提供理论依据。

基于小波时频图和ResNet18的焊接状态监测方法研究

针对焊接过程中因外部干扰因素或焊接参数选择不当而导致的气孔和未熔合缺陷的问题,提出一种小波时频图和深度残差网络(ResNet18)相结合的焊接质量检测方法。首先,搭建管道全位置自动焊接试验平台,利用拾音器记录熔合良好、未熔合和气孔焊接状态下的声音信号,将采集到的声音信号进行小波阈值降噪处理并且计算信号的信噪比,从而得到合适的信号降噪方法。其次,使用连续小波变换得到小波时频图,对时频图进行压缩和预处理,将时频图的大小设置为224×224,并剔除时频图上的标题、坐标和能量等。最后,将处理好的小波时频图作为输入,以未熔合、熔合良好和气孔三种状态作为输出,利用ResNet18网络进行训练。结果表明,该模型对三种焊接状态下的声音信号具有良好的监测效果,其准确率为90.78%。

双Haar小波变换系数的MAP估计及在图像去噪中的应用

小波变换作为一种新的工具,在信号去噪中得到了重要的应用。本文对双Haar小波变换系数,提出了MAP的估计方法,并对其在图像去噪中的应用进行了讨论。实验表明所提出的小波收缩算法与软门限方法相比较,用于图像去噪时可以给出更好的结果。

基于小波变换和CNN的船用机械故障诊断

针对船用机械故障特征自适应提取与智能化诊断问题,采用连续小波变换与卷积神经网络的船舶机械故障诊断方法。以船用风机为例,首先模拟船用机械不同故障并采集振动信号,通过连续小波变换将一维振动信号转化为特征图谱,其包含大量的时频信息。然后通过多次训练后,确定网络结构参数,建立卷积神经网络结构,将时频图作为卷积神经网络输入,挖掘更深层次的高度抽象的故障特征信息。最后在卷积神经网络的输出层接入softmax分类器,实现船用机械的故障诊断。实验结果表明:所提方法能准确识别故障类型,且具有较强的鲁棒性和泛化能力,诊断准确率可达99.3%。与集成经验模态分解、极限学习机故障诊断方法相比,该方法有更高的诊断精度。

基于MAP估计双树复小波的电能质量扰动信号去噪方法

针对电能质量信号的去噪,提出了一种基于MAP估计的双树复小波电能质量扰动信号的去噪方法。首先对带噪信号进行相关性预处理,然后通过MAP方法对双树复小波分解不同层次的细节系数估计噪声方差和信号方差,并计算各层阀值从而得到去噪方案,针对带噪的电压跌落等扰动信号进行仿真,并与传统实小波去噪进行了信噪比和突变点信息保留能力的比较。仿真结果表明,所提算法速度快,去噪效果理想,且易于实现,实用性强,有良好的发展前景。

基于多混沌系统的多图像加密算法

针对多幅图像在传输中的安全性问题,本文提出了一种基于多混沌系统的多图像加密算法.首先,利用离散小波变换对多幅图像进行预处理,得到一幅拼接的大图像;接着,利用logistic-sine-cosine (LSC)映射生成混沌序列,进而生成用于置乱的矩阵O对像素位置进行置乱;最后,采用超混沌Lorenz系统生成四维混沌序列,利用其对置乱后的图像进行双向扩散和行列置乱,获得最终密文图像.所提算法加解密过程简单,执行效率高.实验结果经多方面分析后得出该算法的密钥空间大,可以抵御多种攻击手段,具有较好的加密效果和安全性.

基于离散混沌映射的光纤通信数据置乱加密研究

光纤通信数据一次加密并不能使所有数据呈现置乱状态,数据安全性依旧比较差,所以研究基于离散混沌映射的光纤通信数据置乱加密方法。对原始光纤通信数据展开小波分解,根据骑士巡游理论以及小波子带的特点将全部小波系数置乱,完成光纤通信数据置乱。通过离散混沌映射和Sine映射的离散混沌系统构建混沌序列,利用混沌序列对数据进行一次加密处理,采用位置矩阵对光纤通信数据展开二次加密处理,实现光纤通信数据置乱加密。实验结果表明,所提方法可以有效提升光纤通信数据的安全性,数据加密效果和保密性能良好。

基于小波双三次插值的遥感测绘图像空间分辨率检测方法

为了解决传统图像插值方法在处理效率上的问题,提出了基于小波双三次插值的遥感测绘图像空间分辨率检测方法。利用小波双三次插值将遥感测绘图像分割为空间单位。基于K-L变换原理构建图像滤波系数矩阵。采用异构并行体系,在CUDA架构下进行高密度值计算,实现了遥感测绘图像空间分辨率的快速检测。实验结果表明,本文方法能够在转换图像时保留更多的细节和纹理信息;在不同测绘比例下,能够在2.5 s内完成分辨率检测,且相对水平和垂直分辨率结果较高,适合人眼观察,具有实际应用效果。

基于卷积神经网络的5G 移动通信干扰信号检测

针对5G移动通信信号中存在干扰影响通信性能的问题,提出基于卷积神经网络的5G移动通信干扰信号检测方法。融合软、硬阈值函数优点改进小波阈值函数,对包含干扰信号的5G移动通信信号进行去噪处理,通过傅里叶变换构造时频图并归一化处理,采用引入动量的随机梯度下降算法,训练改进的卷积神经网络,输入归一化后时频图,最终输出干扰信号检测结果。实验结果表明,所提方法去噪能力更强、训练损失更小、训练精度和检测精度更高。