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）.

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.

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.

脉冲射流下气力输送系统特性的数值模拟研究

使用计算流体动力学和离散单元(CFD-DEM)耦合方法,对原管道和加装射流发生器的管道进行数值模拟,通过改变空气速度、射流位置、射流速度以及射流频率,研究颗粒的运动状态。结果表明:在使用脉冲射流的时,颗粒在管道出口的动能显著增加,颗粒由原管道的底部拖曳运动转变为颗粒群悬浮运动,运输系统的能量转换率也显著提高。对管道中不同位置颗粒的波动速度进行频谱分析和连续小波变换分析,结果表明:射流可以有效调节颗粒在管道内运动的周期性,并且减缓管道内颗粒的纵向发展速度,将更多的能量转换为输送系统所需的颗粒轴向速度,进而减小气力输送系统的能耗。

基于传感信号采集的电控发动机振动故障监测方法

通过调理振动信号可以更高效地监测振动故障。为此,提出基于传感信号采集的电控发动机振动故障监测方法。首先,搭建电控发电机传感信号采集与处理架构,通过放大传感信号增益、滤波和转换信号模数的方式处理待监测信号,为提高监测准确性奠定可靠的数据基础。通过小波包分解与重构,获取信号的时域参数和小波能谱熵,并构建三维特征量。然后,利用“一对一”分解策略优化孪生支持向量机,构造多元分类器,使其更适用于振动故障监测这一多类别分类问题,再输入待监测信号的特征量,通过确定故障类别实现持续性监测。仿真结果表明:该方法训练耗时的最大值仅为897 ms,对于转子摩擦振动、不平衡振动等5种类型故障的监测准确率始终在97%以上,在缩减训练样本后准确率仍保持在90%以上。

基于数据挖掘的新旧动能转换成效监测体系研究

采用目前方法构建新旧动能转换成效监测体系时,没有对监测数据进行去噪处理,导致方法的监测精度和敏感度较低。为此,提出基于数据挖掘的新旧动能转换成效监测体系研究方法。首先确定构建新旧动能转换成效监测体系的具体步骤,其次在双树复小波原理的基础上对监测数据进行去噪处理,利用数据挖掘方法构建新旧动能转换成效监测指标体系,并对监测指标进行标准化处理,最后结合熵权法和非线性加权模型完成新旧动能转换成效的监测。实验结果表明所提方法的监测精度和敏感度较高。

Output only modal identification and structural damage detection using time frequency & wavelet techniques

The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom （MDOF） linear time invariant （LTI） and linear time variant （LTV--due to damage） systems based on Time-frequency （TF） techniques--such as short-time Fourier transform （STFT）, empirical mode decomposition （EMD）, and wavelets--is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform （HT） approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they arc signal based; hence, can be used for output only modal identification. A three degree of freedom 1：10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration （white noise） response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

Demodulation Based on Harmonic Wavelet and Its Application into Rotary Machinery Fault Diagnosis

The harmonic wavelet transform（HWT） and its fast realization based on fast Fourier transform（FFT） are introduced. Its ability to maintain the same amplitude-frequency feature is revealed. A new method to construct the time-frequency（TF） spectrum of HWT is proposed, which makes the HWT TF spectrum able to correctly reflect the time-frequency-amplitude distribution of the signal. A new way to calculate the HWT coefficients is proposed. By zero padding the data taken out, the non-decimated coefficients of HWT are obtained. Theoretical analysis shows that the modulus of the coefficients obtained by the new calculation way and living at a certain scale are the envelope of the component in the corresponding frequency band. By taking the cross section of the new TF spectrum, the demodulation for the component at a certain frequency band can be realized. A comparison with the Hilbert demodulation combined with band-pass filtering is done, which indicates for multi-components, the method proposed here is more suitable since it realizes ideal band-pass filtering and avoids pass band selecting. In the end, it is applied to bearing and gearbox fault diagnosis, and the results reflect that it can effectively extract the fault features in the signal.

Local Extrema of Periodic Function’s Wavelet Transform

The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.

APPLICATION OF WAVELET TIME-FR EQUENCY ANALYSIS TO IDENTIFICA-TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.

On Inversion of Continuous Wavelet Transform

This study deduces a general inversion of continuous wavelet transform (CWT) with timescale being real rather than positive. In conventional CWT inversion, wavelet’s dual is assumed to be a reconstruction wavelet or a localized function. This study finds that wavelet’s dual can be a harmonic which is not local. This finding leads to new CWT inversion formulas. It also justifies the concept of normal wavelet transform which is useful in time-frequency analysis and time-frequency filtering. This study also proves a law for CWT inversion: either wavelet or its dual must integrate to zero.

Radar Signal Intra-Pulse Feature Extraction Based on Improved Wavelet Transform Algorithm

With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applicable to the modern radar signal processing, and it is necessary to seek new methods in the two-dimensional transformation domain. The time-frequency analysis method is the most widely used method in the two-dimensional transformation domain. In this paper, two typical time-frequency analysis methods of short-time Fourier transform and Wigner-Ville distribution are studied by analyzing the time-frequency transform of typical radar reconnaissance linear frequency modulation signal, aiming at the problem of low accuracy and sen-sitivity to the signal noise of common methods, the improved wavelet transform algorithm was proposed.

Extraction of MHD Signal Based on Wavelet Transform

Mirnov signals mixed with interferences are a kind of non-stationary signal. It cannot obtain satisfactory effects to extract MHD signals from mirnov signals by Fourier Transform. This paper suggests that the wavelet transform can be used to treat mirnov signals. Theoretical analysis and experimental result have indicated that using the time-frequency analysis characteristics of the wavelet transform to filter mirnov signals can remove effectively interferences and extract useful MHD signals.

Wavelet-Based Response Computation for Base-Isolated Structure under Seismic Excitation

This paper presents a wavelet-based approach for estimating the response of the base-isolated structure under seismic ground motions. The seismic ground motion record is expressed as the multi-scale wavelet coefficients which presents the time frequency characteristics of the seismic excitation. The wavelet domain governing differential equation between the wavelet coefficients of the excitation and response is derived. Numerical study on a one-storey base isolated structure is performed. The result shows that the wavelet based response computation method is of high precision.

Fault Diagnosis for IC Engines Using Wavelet Packet and Image Processing

There are few applications of image processing technology for diagnosing andstate monitoring for internal combustion (IC) engines, which is discussed in detail in this paper.The time-frequency distribution images of cylinder head vibration signals are obtained bydecomposing them with a wavelet packet algorithm. It is the first time that we look attime-frequency distribution images from the point of images. Based on this, a new method forapplying image processing technology for diagnosing and state monitoring for internal combustionengines is presented in this paper. A valve fault diagnosis model is set up by image matching, whichis realized on a four-stroke, six-cylinder diesel engine. At the same time, some notes arepresented in this paper. It has been proved that it is of no good effect to diagnose with histogramsof time-frequency images generated by cylinder head vibration signals that have been processed witha wavelet packet algorithm. The reason is given in this paper. Comparisons of diagnosing effect arecarried out between noise-added signals and original signals. It has little effect on diagnosingresults after signals have been added with noise. The results show that this method has a clearphysical meaning and is of good engineering practicability, feasibility, good precision and highspeed.

Recognizing Breast Cancer Using Edge-Weighted Texture Features of Histopathology Images

Around one in eight women will be diagnosed with breast cancer at some time.Improved patient outcomes necessitate both early detection and an accurate diagnosis.Histological images are routinely utilized in the process of diagnosing breast cancer.Methods proposed in recent research only focus on classifying breast cancer on specific magnification levels.No study has focused on using a combined dataset with multiple magnification levels to classify breast cancer.A strategy for detecting breast cancer is provided in the context of this investigation.Histopathology image texture data is used with the wavelet transform in this technique.The proposed method comprises converting histopathological images from Red Green Blue(RGB)to Chrominance of Blue and Chrominance of Red(YCBCR),utilizing a wavelet transform to extract texture information,and classifying the images with Extreme Gradient Boosting(XGBOOST).Furthermore,SMOTE has been used for resampling as the dataset has imbalanced samples.The suggested method is evaluated using 10-fold cross-validation and achieves an accuracy of 99.27%on the BreakHis 1.040X dataset,98.95%on the BreakHis 1.0100X dataset,98.92%on the BreakHis 1.0200X dataset,98.78%on the BreakHis 1.0400X dataset,and 98.80%on the combined dataset.The findings of this study imply that improved breast cancer detection rates and patient outcomes can be achieved by combining wavelet transformation with textural signals to detect breast cancer in histopathology images.

面向电力通信光缆的典型故障精准定位方法

在电力系统中,通信是必不可少的,用于电力系统的监控、保护、控制等环节。电力通信光缆作为实现电力系统与通信系统之间互联的重要组成部分,在电力系统中得到广泛应用。针对电力通信光缆故障,不同故障模式可能具有不同的影响和特征,为避免由光缆故障导致的电力通信异常,提出面向电力通信光缆的典型故障精准定位方法。建立电力通信光缆网络信道变换模型,生成电力通信光缆多径信道数据传递函数。引进小波转换算法,对电力通信光缆传输信号进行小波转换。设定信号在空间中的尺度因子,以此为依据提取转换后的信号极值点。根据故障点测量站的位置,精准定位电力通信光缆典型故障。对比实验结果表明,设计的方法可以实现对电力通信光缆典型故障的精准定位。