检测脑电癫痫波的小波分析方法

小波分析是一种时 /频域的分析方法。它具有多分辨率 ,相对带宽恒定 ,在时、频两域都具有表征信号局部特征能力的特点 ,被誉为“数学显微镜”。本文基于二进小波变换 ,对嫌疑癫痫波进行多尺度的分析 ,根据脑电嫌疑波的三种基本成分 (棘波、尖波和慢波 )在不同尺度上的特性检测出它们。文中最后给出了小波分析检测脑电癫痫波的实例。理论和实践表明 ,小波分析在脑电癫痫波的检测中有广阔的应用前景。

Wavelet analysis of pressure fluctuation signals in a gas-solid fluidized bed

It has been shown that much dynamic information is hidden in the pressure fluctuation signals of a gas-solid fluidized bed. Unfortunately, due to the random and capricious nature of this signal, it is hard to realize reliable analysis using traditional signal processing methods such as statistical analysis or spectral analysis, which is done in Fourier domain. Information in different frequency band can be extracted by using wavelet analysis. On the evidence of the composition of the pressure fluctuation signals, energy of low frequency (ELF) is proposed to show the transition of fluidized regimes from bubbling fluidization to turbulent fluidization. Plots are presented to describe the fluidized bed's evolution to help identify the state of different flow regimes and provide a characteristic curve to identify the fluidized status effectively and reliably.

Multi-resolution graph-based clustering analysis for lithofacies identifi cation from well log data: Case study of intraplatform bank gas fi elds, Amu Darya Basin

In this study, we used the multi-resolution graph-based clustering （MRGC） method for determining the electrofacies （EF） and lithofacies （LF） from well log data obtained from the intraplatform bank gas fields located in the Amu Darya Basin. The MRGC could automatically determine the optimal number of clusters without prior knowledge about the structure or cluster numbers of the analyzed data set and allowed the users to control the level of detail actually needed to define the EF. Based on the LF identification and successful EF calibration using core data, an MRGC EF partition model including five clusters and a quantitative LF interpretation chart were constructed. The EF clusters 1 to 5 were interpreted as lagoon, anhydrite flat, interbank, low-energy bank, and high-energy bank, and the coincidence rate in the cored interval could reach 85%. We concluded that the MRGC could be accurately applied to predict the LF in non-cored but logged wells. Therefore, continuous EF clusters were partitioned and corresponding LF were characteristics ＆different LF were analyzed interpreted, and the distribution and petrophysical in the framework of sequence stratigraphy.

Study on spillover effect of copper futures between LME and SHFE using wavelet multiresolution analysis

Research on information spillover effects between financial markets remains active in the economic community. A Granger-type model has recently been used to investigate the spillover between London Metal Exchange(LME) and Shanghai Futures Exchange(SHFE) ,however,possible correlation between the future price and return on different time scales have been ignored. In this paper,wavelet multiresolution decomposition is used to investigate the spillover effects of copper future returns between the two markets. The daily return time series are decomposed on 2n(n=1,…,6) frequency bands through wavelet mul-tiresolution analysis. The correlation between the two markets is studied with decomposed data. It is shown that high frequency detail components represent much more energy than low-frequency smooth components. The relation between copper future daily returns in LME and that in SHFE are different on different time scales. The fluctuations of the copper future daily returns in LME have large effect on that in SHFE in 32-day scale,but small effect in high frequency scales. It also has evidence that strong effects exist between LME and SHFE for monthly responses of the copper futures but not for daily responses.

Lifting transform via Savitsky-Golay filter predictor and application of denoising

The Savitsky-Golay filter isa smoothing filter based on polynomial regression.Itemploys the regression fitting capacity to improve the smoothing results.But Savit-sky-Golay filter uses a fix sized window.It has the same shortage of Window FourierTransform.Wavelet mutiresolution analysis may deal with this problem.In this paper,tak-ing advantage of Savitsky-Golay filter's fitting ability and the wavelet transform's multiscaleanalysis ability,we developed a new lifting transform via Savitsky-Golay smoothing filteras the lifting predictor,and then processed the signals comparing with the ordinary Savit-sky-Golay Smoothing method.We useed the new lifting in noisy heavy sine denoising.Thenew transform obviously has better denoise ability than ordinary Savitsky-Golay smooth-ing method.At the same time singular points are perfectly retained in the denoised signal.Singularity analysis,multiscale interpolation,estimation,chemical data smoothing andother potential signal processing utility of this new lifting transform are in prospect.

Fingerprint Liveness Detection Based on Multi-Scale LPQ and PCA

Fingerprint authentication system is used to verify users' identification according to the characteristics of their fingerprints.However,this system has some security and privacy problems.For example,some artificial fingerprints can trick the fingerprint authentication system and access information using real users' identification.Therefore,a fingerprint liveness detection algorithm needs to be designed to prevent illegal users from accessing privacy information.In this paper,a new software-based liveness detection approach using multi-scale local phase quantity(LPQ) and principal component analysis(PCA) is proposed.The feature vectors of a fingerprint are constructed through multi-scale LPQ.PCA technology is also introduced to reduce the dimensionality of the feature vectors and gain more effective features.Finally,a training model is gained using support vector machine classifier,and the liveness of a fingerprint is detected on the basis of the training model.Experimental results demonstrate that our proposed method can detect the liveness of users' fingerprints and achieve high recognition accuracy.This study also confirms that multi-resolution analysis is a useful method for texture feature extraction during fingerprint liveness detection.

Denoising Method for Shear Probe Signal Based on Wavelet Thresholding

Shear probe works under a tough environment where the turbulence signals to be measured are very weak. The measured turbulence signals often contain a large amount of noise. Due to wide frequency band, noise signals cannot be effectively removed by traditional methods based on Fourier transform. In this paper, a wavelet thresholding denoising method is proposed for turbulence signal processing in that wavelet analysis can be used for multi-resolution analysis and can extract local characteristics of the signals in both time and frequency domains. Turbulence signal denoising process is modeled based on the wavelet theory and characteristics of the turbulence signal. The threshold and decomposition level, as well as the procedure of the turbulence signal denoising, are determined using the wavelet thresholding method. The proposed wavelet thresholding method was validated by turbulence signal denoising of the Western Pacific Ocean trial data. The results show that the propsed method can reduce the noise in the measured signals by shear probes, and the frequency spectrums of the denoised signal correspond well to the Nasmyth spectrum.

Non-classical Algorithm for Time Series Prediction of the Range of Economic Phenomena With Regard to the Interaction of Financial Market Indicators

The aim of the article is to present non-clasical copyrighted algorithm for prediction of time series, presenting macroeconomic indicators and stock market indices. The algorithm is based on artificial neural networks and multi-resolution analysis （the algorithm is based on Daubechies wavelet）. However, the main feature of the algorithm, which gives a good quality of the forecasts, is all included in the series analysis division into, a few partial under-series and prediction dependence on a number of other economic series. The algorithm used for the prediction, is copyrighted algorithm, labeled M.H-D in this article. Application of the algorithm was performed on a series presenting WIG 20. The forecast of WIG 20 was conditional on trading the Dow Jones, DAX, Nikkei, Hang Seng, taking into account the sliding time window. As an example application of copyrighted model, the forecast of WIG 20 for a period of two years, one year, six month was appointed. An empirical example is described. It shows that the proposed model can predict index with the scale of two years, one year, a half year and other intervals. Precision of prediction is satisfactory. An average absolute percentage error of each forecast was： 0.0099%---for two-year forecasts WIG 20; 0.0552%--for the annual forecast WIG 20; and 0.1788%---for the six-month forecasts WIG 20.

A framework of region-based dynamic image fusion

A new framework of region-based dynamic image fusion is proposed. First, the technique of target detection is applied to dynamic images (image sequences) to segment images into different targets and background regions. Then different fusion rules are employed in different regions so that the target information is preserved as much as possible. In addition, steerable non-separable wavelet frame transform is used in the process of multi-resolution analysis, so the system achieves favorable characters of orientation and invariant shift. Compared with other image fusion methods, experimental results showed that the proposed method has better capabilities of target recognition and preserves clear background information.

Numerical Simulation for Accuracy of Velocity Analysis in Small-Scale High-Resolution Marine Multichannel Seismic Technology

When used with large energy sparkers, marine multichannel small-scale high-resolution seismic detection technology has a high resolution, high-detection precision, a wide applicable range, and is very flexible. Positive results have been achieved in submarine geological research, particularly in the investigation of marine gas hydrates. However, the amount of traveltime difference information is reduced for the velocity analysis under conditions of a shorter spread length, thus leading to poorer focusing of the velocity spectrum energy group and a lower accuracy of the velocity analysis. It is thus currently debatable whether the velocity analysis accuracy of short-arrangement multichannel seismic detection technology is able to meet the requirements of practical application in natural gas hydrate exploration. Therefore, in this study the bottom boundary of gas hydrates(Bottom Simulating Reflector, BSR) is used to conduct numerical simulation to discuss the accuracy of the velocity analysis related to such technology. Results show that a higher dominant frequency and smaller sampling interval are not only able to improve the seismic resolution, but they also compensate for the defects of the short-arrangement, thereby improving the accuracy of the velocity analysis. In conclusion, the accuracy of the velocity analysis in this small-scale, high-resolution, multi-channel seismic detection technology meets the requirements of natural gas hydrate exploration.

The Construction of a Class of Compactly Supported Orthogonal Matrix-valued

In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.

The Study on Scaling Function of L^2(R^s)

In this paper, using the orthonormal multiresolution analysis（MRA） of L^2（R^s）, we get two important properties of the scaling function with dilation matrix A = MI of L^2 （R^s）. These properties axe chaxacterized by some inequalities and equalities.

Analysis on electric energy measuring method based on multi-resolution analysis

Along with the massive applications of the non-linear loads and the impact loads, many non-stationary stochastic signals such as harmonics, inter-harmonics, impulse signals and so on are introduced into the electric network, and these non-stationary stochastic signals have had effects on the accuracy of the measurement of electric energy. The traditional method like Fourier Analysis can he applied efficiently on the stationary stochastic signals, hut it has little effect on non-stationary stochastic signals. In light of this, the form of the signals of the electric network in wavelet domain will he discussed in this paper. A measurement method of active power based on multi-resolution analysis in the stochastic process is presented. This method has a wider application scope compared with the traditional method Fourier analysis, and it is of good referential value and practical value in terms of raising the level of the existing electric energy measurement.

Application of wavelet analysis to fault diagnosis of angular measuring system

For fault diagnosis, signal singularity and irregularity discontinuity fraction are very significant characteristics of signal. The discontinuity of output signal represents a system fault . In an angular measuring system, function transformer uses two D/A convertors, output circuit fault of a D/A convertor brings about discontinuity of one phase input voltage amplitude of inductosyn, results in a system error exceeding the allowable error and reduces the system accuracy. This is the reason why discontinuity is detected. Fourier transform has no resolution ability in angular domain, but wavelet can analyse signal in angular and frequency domains. So we decompose the error signal of angular measuring system by wavelet, detect the signal singularity at high frequency layer and find out the accurate position of it.

Fault Feature Extraction of Rotating Machinery Based on Wavelet Transformation and Multi-resolution Analysis

This paper expounded in detail the principle of energy spectrum analysis based on discrete wavelet transformation and multiresolution analysis. In the aspect of feature extraction method study, with investigating the feature of impact factor in vibration signals and considering the non-placidity and non-linear of vibration diagnosis signals, the authors import wavelet analysis and fractal theory as the tools of faulty signal feature description. Experimental results proved the validity of this method. To some extent, this method provides a good approach of resolving the wholesome problem of fault feature symptom description.

Implementation of Adaptive Wavelet Thresholding Denoising Algorithm Based on DSP

By utilizing the capability of high-speed computing,powerful real-time processing of TMS320F2812 DSP,wavelet thresholding denoising algorithm is realized based on Digital Signal Processors.Based on the multi-resolution analysis of wavelet transformation,this paper proposes a new thresholding function,to some extent,to overcome the shortcomings of discontinuity in hard-thresholding function and bias in soft-thresholding function.The threshold value can be abtained adaptively according to the characteristics of wavelet coefficients of each layer by adopting adaptive threshold algorithm and then the noise is removed.The simulation results show that the improved thresholding function and the adaptive threshold algorithm have a good effect on denoising and meet the criteria of smoothness and similarity between the original signal and denoising signal.

Research on the detecting methods of singularity in deformation signal based on two kinds of wavelet entropy

There are various influencing factors that affect the deformation observation, and deformation signals show differ- ent characteristics under different scales. Wavelet analysis possesses multi-scale property, and the information entropy has great representational capability to the complexity of information. By hamming window to the wavelet coefficients and windowed wavelet energy obtained by multi-resolution analysis （MRA）, it can be achieved to measure the wavelet time entropy （WTE） and wavelet energy entropy （WEE）. The paper established deformation signals, selected the parameters, and compared the sin- gularity detection ability and anti-noise ability of two kinds of wavelet entropy and applied them to the singularity detection at the GPS continuously operating reference stations. It is shown that the WTE performs well in weak singularity information de- tection in finite frequency components signals and the WEE is more suitable for detecting the singularity in the signals with complex, strong background noise.

A hexahedron element formulation with a new multi-resolution analysis

A multiresolution hexahedron element is presented with a new multiresolution analysis(MRA)framework.The MRA framework is formulated out of a mutually nesting displacement subspace sequence,whose basis functions are constructed of scaling and shifting on element domain of a basic node shape function.The basic node shape function is constructed from shifting to other seven quadrants around a specific node of a basic isoparametric element in one quadrant and joining the corresponding node shape functions of eight elements at the specific node.The MRA endows the proposed element with the resolution level(RL)to adjust structural analysis accuracy.As a result,the traditional 8-node hexahedron element is a monoresolution one and also a special case of the proposed element.The meshing for the monoresolution finite element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the solid mathematical basis.The simplicity and clarity of shape function construction with the Kronecker delta property and the rational MRA enable the proposed element method to be more rational,easier and efficient in its implementation than the conventional mono-resolution solid element method or other MRA methods.The multiresolution hexahedron element method is more adapted to dealing with the accurate computation of structural problems.

Homogeneous wavelets and framelets with the refinable structure

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this paper, we provide a comprehensive study on connecting homogeneous wavelets and framelets to nonhomogeneous ones with the refinable structure. This allows us to understand better the structure of homogeneous wavelets and framelets as well as their connections to the refinable structure and multiresolution analysis.