Continuous wavelet transform and exactly solvable model of nonstationary signals

An analytic expression for a continuous wavelet transform (CWT) is obtained for a nonstationary signal with spectral properties varying with time. As a model of the nonstationary signal, a superposition of elementary nonstationary signals is considered, each of which is the product of the Gaussian-shape envelope and an oscillating function. To obtain the CWT, the mother Morlet wavelet is used. The result is compared with the window Fourier transform (Gabor transform).The advantages of the CWT are illustrated by concrete examples. The applications of the exactly solvable model of nonstationary signals for simulating transient processes in physics are considered.     

Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis

We present the symbolic resonance analysis (SRA) as a viable method for addressing the problem of enhancing a weakly dominant mode in a mixture of impulse responses obtained from a nonlinear dynamical system. We demonstrate this using results from a numerical simulation with Duffing oscillators in different domains of their parameter space, and by analyzing event-related brain potentials (ERPs) from a language processing experiment in German as a representative application. In this paradigm, the averaged ERPs exhibit an N400 followed by a sentence final negativity. Contemporary sentence processing models predict a late positivity (P600) as well. We show that the SRA is able to unveil the P600 evoked by the critical stimuli as a weakly dominant mode from the covering sentence final negativity.     

结合小波分析法与导数光声光谱技术测量弱光谱信号的实验研究

结合导数光声光谱技术与小波分析方法,精确测量了光声光谱中的弱光谱信号.首先利用自己设计的仪器装置实现光声光谱的一阶导数,在此基础上,根据导数光声光谱的数据选择合理的分析小波,将光声光谱信号分解为不同频率信号的叠加,被分解的信号满足线性性质且原信号的峰值信息保持不变,由频率的差异可区分出光声信号和噪声信号,从而提取出光声光谱中的弱光谱信号.结合物理方法与软件方法的分析结果,准确地测量了氙灯的输出光声光谱中3个不明显的弱峰值,位置分别为699.7nm、753.4nm和776.5nm.该方法可以更准确地提取出光声光谱的峰值信息,有效地提高了光声光谱的测量精度,为光声光谱分析法在生物医学及化学分析中的应用提供了一种更精确的分析方法.     

Direct analysis of in-line particle holograms by using wavelet transform and envelope reconstruction method

We propose a new digital method for sizing particles and tracking their positions from an in-line hologram by using a combination of a wavelet transform and a reconstruction of the envelope functions. In the proposed method, the hologram is recorded by a charge-coupled device (CCD) sensor. The wavelet transform of digitized holograms gives information about the position of particles, while the reconstruction of envelope functions provides the size of particles. Preliminary theoretical and experimental verifications are presented. The system limitation of the method is discussed.     

A method for statistical wavelet analysis of ionospheric GPS signals

A technique of statistical wavelet analysis is proposed and tested for applicability to the data of radio sounding of the ionosphere by navigation signals of the global positioning system. Important advantages of wavelet analysis over spectral analysis are demonstrated, including performance under short-term fault conditions.     

Instantaneous intensity analysis of impulsive sound by the wavelet transform

The method for measuring instantaneous intensity by using the wavelet transform is proposed. We also conducted an analysis of the experimental data by using the hammering noise and confirmed the applicability of this calculation method.     

Detecting emboli from Doppler ultrasound signals with the wavelet packet analysis method

A Doppler ultrasound analysis method based on wavelet package transform was proposed for embolic detection. The embolic Doppler signal was firstly decomposed using the wavelet packet. Then the sensitive characteristics were calculated from each sub-band signal and used in the emboli classification. This method was applied to analyze 300 cases simulated and 163 cases clinical Doppler signals. The minimum error ratio of embolic detection using this method was 13 percents lower than that using the traditional spectrogram analysis method.It was shown that this method overcame the limit between the time and frequency resolution in the short time Fourier transform, improved the accuracy of embolic detection greatly and extracted more reliable parameters for the clinical diagnosis.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

Extraction of signals from white and colored noise using the discrete wavelet transform

Methods based on wavelet analysis are used to study longitudinal elastic waves propagating in aluminum single crystals in the [111] and [001] directions at frequencies of 5 and 10 MHz. Results of the wavelet filtering of responses of the laser Doppler interferometer to these acoustic signals are reported. The efficiency of filtering the time dependencies of the interferometer response in the presence of white and colored noise is studied. Recommendations concerning the choice of the filtering parameters are given.     

Statistical searching of deformation phases on wavelet transform maps of fringe patterns

A wavelet transform (WT) analysis is presented to obtain the deformation phases from the fringes with non-uniform carrier frequency, which may appear in the pattern of varied-periodic fringes generated in displacement measurement. Based on the phase maps of the Morlet WT coefficients distributed in a space-scale spectrum, a statistical processing is carried out to search the compacted density of the phase intervals over the scale, and from that the phase modulations related to the object deformation can be determined. Numerical simulation demonstrates the validity of the pattern-processing technique, and the experimental results show the applications to the measurement of the in-plane displacement by the digital speckle pattern interferometry (DSPI) and the measurement of the out-of-plane deflection by the projecting Moiré fringes.     

Features of underwater echo extraction based on the stationary wavelet transform and singular value decomposition

A feature extraction method of underwater echo is proposed, which uses the redundancy property of SWT (the Stationary Wavelet Transform) and the steady property of SVD (Singular Value Decomposition). Since using singular values of SWT coefficients matrix as feature vectors, with the K-L transform to multi-subspace signal obtained from SWT, it is a feature compression method essentially. In contrast to the method of sub-bands energy feature based on discrete orthogonal wavelet transform (DWT), better results of lake trial data are acquired with this method: (1) Under the same sample and distance within-class, distance between-class is larger than former; (2) Correct recognition rates are also higher than former, whether the training and testing samples are chosen from the same lake trail or not; (3) Sample sets varying, the variation range of correct recognition rates is far less than the former. Thus this method can obtain more robust, effective features and better correct recognition results.     

一种新的基于小波变换的图像去噪方法

根据图像小波分解的特点和小波分解后高频小波系数的统计特性,构造了一种新阈值函数的去噪算法。与传统的硬阈值、软阈值函数相比,新阈值函数考虑了图像能量分布的特点,对于每一小波系数乘以一个与自身大小相关的降噪因子,并且新阈值函数简单易于计算,具有较强的自适应性。实验结果表明,采用新阈值函数的去噪结果能够有效地抑制图像的马赛克效应,无论在视觉效果上,还是在信噪比增益上均优于传统的软、硬阈值方法。     

基于小波变换的新型数字散斑相关方法

通过将小波分析的方法应用到传统的空域相关计算中,提出了基于小波变换的数字散斑相关方法。详细介绍了该方法的原理,并对传统空域相关方法与小波相关方法进行了实验计算比较。实验结果表明,与传统的空域相关方法相比,基于小波变换的数字散斑相关方法大大提高了相关计算的精度,精度由0 05像素提高到了0 01像素以下。最后利用该方法测量了编织结构复合材料板在三点弯曲载荷作用下的位移场。     

3-D surface profilometry based on modulation measurement by applying wavelet transform method

A new analysis of 3-D surface profilometry based on modulation measurement technique by the application of Wavelet Transform method is proposed. As a tool excelling for its multi-resolution and localization in the time and frequency domains, Wavelet Transform method with good localized time-frequency analysis ability and effective de-noizing capacity can extract the modulation distribution more accurately than Fourier Transform method. Especially for the analysis of complex object, more details of the measured object can be well remained. In this paper, the theoretical derivation of Wavelet Transform method that obtains the modulation values from a captured fringe pattern is given. Both computer simulation and elementary experiment are used to show the validity of the proposed method by making a comparison with the results of Fourier Transform method. The results show that the Wavelet Transform method has a better performance than the Fourier Transform method in modulation values retrieval.     

Phase retrieval of optical fringe patterns from the ridge of a wavelet transform

A new method for phase retrieval of optical fringe patterns is presented. This method is based on a wavelet transform and is capable of extracting the full 2D phase distribution from a single fringe pattern. An important conclusion that the phase of the optical fringe pattern is equal to the phase of its wavelet transform on the ridge of the wavelet transform is theoretically clarified. The method is compared with the Fourier transform and the integration methods. A numerical simulation and an experimental example of phase retrieval are shown.     

Application of wavelet transform in feature extraction and pattern recognition of wideband echoes

1IntroductionThefeatureextractionofunderwaterobjectsfromactiveechoisadifficultproblem.Thereceivedsignalisaconvolutionofthetransmittedsignalwiththeimpulseresponseoftheob-jects,plusvariousadditivedisturbances,includingnoiseandresonance.Inordertorecognizetheobjectswehavetoextractimportantfeaturesfromtheechoes.Inrecentyearsmanymeth-odshavebeenproposed,andoneoftheapproachesistodeconvolvetheechotogettheimpuIseresponsesequenceoftheobject.Thisisoftenfollowedbyaparametermodelapproximationwhiletheestim…     

基于数字全息与小波变换的图像数字水印技术

提出一种以数字全息和小波变换为基础的数字水印技术,实现在原始图像中嵌入数字全息水印。首先通过傅里叶变换方法将待隐藏的图像制成数字全息水印图,接着将数字全息水印图和原始图像都分为四个子块,并对原始图像子块进行小波分解,最后将数字全息图像子块嵌入到原始图像相应子块较大的小波系数中。实验仿真结果证明了该水印技术对图像剪切和图像有损压缩有较好的稳定性。     

Roller bearing acoustic signature extraction by wavelet packet transform,applications in fault detection and size estimation

Continuous online monitoring of rotating machines is necessary to assess real-time health conditions so as to enable early detection of operation problems and thus reduce the possibility of downtime. Rolling element bearings are crucial parts of many machines and there has been an increasing demand to find effective and reliable health monitoring technique and advanced signal processing to detect and diagnose the size and location of incipient defects. Condition monitoring of rolling element bearings, comprises four main stages which are, statistical analysis, fault diagnostics, defect size calculation, and prognostics. In this paper the effect of defect size, operating speed, and loading conditions on statistical parameters of acoustic emission (AE) signals, using design of experiment method (DOE), have been investigated to select the most sensitive parameters for diagnosing incipient faults and defect growth on rolling element bearings. A modified and effective signal processing algorithm is designed to diagnose localized defects on rolling element bearings components under different operating speeds, loadings, and defect sizes. The algorithm is based on optimizing the ratio of Kurtosis and Shannon entropy to obtain the optimal band pass filter utilizing wavelet packet transform (WPT) and envelope detection. Results show the superiority of the developed algorithm and its effectiveness in extracting bearing characteristic frequencies from the raw acoustic emission signals masked by background noise under different operating conditions. To experimentally measure the defect size on rolling element bearings using acoustic emission technique, the proposed method along with spectrum of squared Hilbert transform are performed under different rotating speeds, loading conditions, and defect sizes to measure the time difference between the double AE impulses. Measurement results show the power of the proposed method for experimentally measuring size of different fault shapes using acoustic emission signals.     

基于特征点的整数小波目标跟踪方法的研究

基于提升方法的整数小波变换的诸多优点,以Harr整数小波变换为例,提出了动态目标跟踪算法。对标准图像进行整数Harr小波变换,并将提升项取整,对提升项的参数用一定数量训练图像进行学习。选取在训练参数平方和为最小意义上的、使整数小波变换后的图像高频部分具有较大值的点作为特征点。对包含有目标的参考图像进行整数小波变换,选择高频分量具有较大值的点,利用训练过的提升项参数使目标和基准图像配准。由于算法采用整数小波变换,使提取具有较好的鲁棒性,从而实现目标发生旋转、平移及尺度变化等的跟踪过程。仿真实验表明,该方法能对动态运动目标进行跟踪。     

Uncertainty analysis of whole-field phase-differences retrieved from ESPI fringe patterns by using the Fourier transform method (FTM)

We have evaluated the uncertainty associated with the whole-field phase-differences retrieved by using the Fourier transform method (FTM), from a fringe pattern generated by electronic speckle pattern interferometry (ESPI). The phase-differences were induced by applying load to an elastic sample. The FTM involved the Fourier transform application to the fringe pattern, the isolation of the term carrying the phase information by applying a band-pass filter in the spatial frequency domain, and then the inverse Fourier transform application. Since the fringes in the analyzed pattern were adequately open, the FTM outcomes were presumed to be mainly affected by errors in the determination of both the width and the location of the applied filter mask. The influence of these error sources was assessed by using a Monte Carlo-based computer simulation. It implied evaluating the phase-differences a large number of times under the influence of the involved error sources. We found that the phase uncertainty depends strongly on the width of the applied filter mask; the influence of the other error sources considered into the uncertainty propagation was significantly smaller.