Multiresolution Wavelet Transform for Detection of EEG Abnormal Rhythms

The signal of brain activity is a non-stationary random signal including lots of physiology and disease information, which is of important action for doctors to judge pathological changes in brain. So the analysis and process of the EEG signals are always attended. In this paper, the authors take account of the time-frequency localization of wavelet transform and use multiresolution wavelet transform to detect EEG abnormal rhythms. The signals of different scales after EEG signals are transformed by multiresolution wavelet transform not only reflect the frequency information of the signals, namely the more great scale is the lower of the frequency of the signals,but also reflect the time information of the signals, namely EEG state at that time. The test results indicate that the abnormal rhythms of the EEG signals can be detected effectively if right wavelet basis is selected.     

Application of Wavelet Transform to De-noising Method

The wavelet transform is a new subject developed quickly in the past ten years. Compared with the Fourier transform, the wavelet transform is a part of time-frequency transform. The most important character is that it can be used to transform a signal into basic units at different scales and location, each unit represents a component of original signal difference from others. The wavelet transform has been proven to be a powerful and efficient tool for processing signal due to this character. This paper introduces the de-noising principles of the wavelet transform. It is proved to be an effective method by the simulating analysis.     

Application of the Wavelet Transform to the Pulse Signal Analysis of Druggers

According to the randomness of human pulse signals,the multiresolution analysis of the wavelet transform is used to analyze such signals.Its purpose is to extract the abnormal information from the pulse signals of heroin druggers and to obtain the primary judgment criterion which can be used to identify druggers from healthy persons.The scale spectrum based on the wavelet transform of pulse signals carries the important characteristic information of the health situation of human body.The pulse signals of 15 heroin druggers and 15 healthy persons are analyzed and the scale spectrum and the total signal energy of every signal are extracted.It is found that the ratio between the sum(i.e.,scale-wavelet energy) of the scale spectrum in a specific scale-time region and the total signal energy for heroin druggers is generally higher than that of healthy persons.Using the percentage of the ratio between the scale-wavelet energy in the specific scale-time region and the total signal energy as characteristic parameter,a critical parameter is determined that is used to classify heroin druggers and healthy persons.Thus,all of the 15 healthy persons are identified correctly from 30 subjects.Only two heroin persons are misjudged.The experiment results of classification show that the method presented is feasible and effective for detecting the pulse abnormalities of heroin druggers.     

EEG Signal Denoising Based on Wavelet Transform

The article focuses on the method of noise cancellation for EEG signal. The method of notch filter is discussed. According to the frequency of noise and the principle of notch filter, the design result of the notch filter and the denoised signal are presented. Then, the analysis of EEG signal are proposed based on wavelet transform (WT) and noise cancellation using WT. Wavelet transform is a multi-resolution time-frequency analysis method. It can decompose mixed signal into signals at different frequency bands. The EEG signal is analyzed and denoised using WT, then the results are presented respectively. Comparing the experiment results shows that WT can detect and process noise in the EEG signal effectively.     

The Signals Analysis System Based on Fast Wavelet Transform

The fast wavelet transform (FWT) algorithm in wavelet analysis was introduced in the paper. With quadrature mirror filters (QMF) associated with popular wavelet bases, the fast wavelet decomposition and reconstruction for signals were implemented. Combined with virtual instrument technique, the FWT analysis system for signals was successfully developed. The system can break up signal not only into approximations, which are the high-scale and low-frequency components of the signal, but also into details which are the low-scale and high-frequency components. Especially it can identify singularity signal, which contain some important message of equipment condition and fault, and refine signal from noisy signal, which is corrupted by noise.     

Framework of M-channel Systems and the Best Symmetric Extension

In image compression based on wavelet transform, the borders of images have to be processed in advance so as to reduce the distortions around the borders. An efficient way for this problem is symmetric extension. There are different types of symmetric extension methods. The paper presents the best symmetric extension and gives a design algorithm. Using the algorithm, we obtain the scheme of extending and windowing the signals in general best M-channel analysis/synthesis system.     

Frequency domain analysis and the application for extracting electroencephalogram signal characteristic waves

A new quantitative analysis method to describe the dynamic variation of electroencephalogram (EEG) signals was proposed. Based on the Fourier transformation, the method is called Fourier multi resolution analysis (FMRA). FMRA decomposes the frequency domain with a binary system and can resolve EEG signals into the basic rhythms of the four waves to study the dynamic characteristics of EEG signal rhythms. FMRA has clear physical meaning, and can obtain more information than wavelet multi resolution analysis does. FMRA can extract perfectly the rhythmic characteristics of EEG signals in the time and frequency domains.     

Wavelet Packet Decomposition Based on Entropy Threshold for White-noise Rejection in PD Signal

This paper analyzes the different characteristics of white-noise interference in the signals of partial discharge (PD) after wavelet transform. There is high value in lots of scales for PD and white-noise interference is to zero with increasing scale. The threshold is set for wavelet coefficient in all scales. If the coefficient of signal is higher than the threshold, it is PD signal. Otherwise it is noise interference. A threshold-based wavelet packet transform (WPT) algorithm is put forward to suppress white noise interference in PD signals. The results testifies that it has a favorable adaptability to extract PD signals using WPT.     

Filtering Construct of Adaptive Filter Grou Pwith Multi-scale Decomposition

The principle and method of the adaptive filter and the filtering with wavelet transform were analyzed, and the model and method of adaptive filtering with wavelet transforms for the transient signal was established. The separated noise of signal by the multi-scale decomposition of wavelet transforms, was the input signal of adaptive filter, and accordingly the optimal filtering method of signal-noise decomposition was realized. By the adaptive filter grou Pbased on the wavelet transform, the optimal filtering to the multi-noise of signal is achieved at the same time, and the method presented in this paper has the excellent filtering capability. Examples of application demonstrate that this method presented is excellent to realize the optimal estimate to the valuable signal and noise of the transient signal in the same frequency segment.     

Speedy Recognition of Noise in Real Time Signal Based on Wavelet Transform

It's necessary to process position and gesture of rocket on real time within the flight of rocket. This work should base exact data. But much noise has been found in the data and the noise recognize is regarded as a focus. A speedy online arithmetic recognizing noise is proposed based on wavelet transform. The computing complexity measured by time of this arithmetic is a constant which is greatly reduces the works of calculation of wavelet transform. It can recognize the noise fast when the signal is gathered. The applications in these problems show that the effective arithmetic satisfies the needs of real time and can handle the real time data measured in other yields.     

Application of Time-frequency Representations in Study on Heart Sound

Heart sound is non-stationary signal, some of its important characteristics can be obtained by time - frequency analysis method. The criteria of different time-frequency representation concentricity of spectrogram, coverage, MSE and regularity of time envelope axe proposed, the performances of Short-time Fourier transform, Wigner - Ville distribution, continuous wavelet transform, and S transform in study on heart sound are compared based on these criteria , and concrete example of application is given.     

A Virtual Wavelet Transform Analyzer for the Signal Analysis Based on the Direct Algorithm

A virtual wavelet transform analyzer for the signal analysis based on the direct algorithm is introduced so that the discrete wavelet transform and continuous wavelet transform is maken to signal in the direct algorithm. The authors first introduce the direct algorithm of the WT, which is numerical algorithm obtained from the original formula of the wavelet transform by directly numericalizing. Then some conclusions are drawn on the direct algorithm. The examples are the sampling principle and technology for the wavelets, the limitation of the scale range of the wavelets and the measures to solve the edge phenomenal in the direct algorithm of the discrete wavelet transform, and some conclusions in the direct algorithm of the continuous wavelet transform. The virtual wavelet transform analyzer for the signal analysis based on the direct algorithm explored based on these studies and combined with virtual instrument technique can make the discrete wavelet transform and continuous wavelet transform to signal with any basic wavelet. It can be applied in studying the property of any basic wavelet and learning the theory on the wavelet transform, and also in making some engineering signal analysis. In the end, the authors give some typical examples for the application of the virtual analyzer. These examples show that the analyzer can be applied in many situations.     

Wavelet Analysis of Electrically Evoked Surface Electromyography Signals During Muscle Fatigue

By analysis of electricallyevoked surface electromyogram(SEMG) to suralmuscle, study the characteristics of SEMG signal during muscle fatigue. The time stretchingof two semi-ave of M-wave are analyzed respectively by wavelet method choosing wavelet function matching to M-wave. Indexes of muscle fatigue are educed accordingto the scale of wavelet transform, are the quantitative analysis is realized during muscle fatigue. This method overcomes the limitation of Fourier Transform that it has no resolution in time domain, find indicators of SEMG which are correct, reliable and easy to interpret, and try to providetheoretic referencefor the applicationsof these indicators.     

FTIR结合小波变换分析鉴别8种根茎类作物

为了区分鉴别8种根茎类作物,通过采用傅里叶变换红外光谱(FTIR)结合小波变换(WI)、主成分分析(PCA)和聚类分析(HCA)的方法,测试研究了8种根茎类作物40个样品的红外光谱。结果表明：8种样品红外图谱相似,但在1800~700 cm-1范围内,红外光谱的峰位、峰形及吸收强度差异明显。对此范围内的原始红外光谱进行连续小波和离散小波变换。提取连续小波变换的第15层系数和离散小波变换的第5尺度细节系数数据,进行主成分分析和聚类分析。连续小波和离散小波的前3个主成分的累计贡献率分别为93.12%、89.78%,主成分分析和聚类分析正确率为100%。最终结果显示：傅里叶变换红外光谱技术结合小波变换的方法可以区分鉴别不同种的根茎类作物。     

Application limitation of the Hilbert Huang transform to earthquake ground motion analysis

We presented herein detailed comparison between emulational and real earthquake signals. Intrinsic Mode Functions (IMF) were regarded as products of the empirical mode decomposition (EMD) during Hilbert Huang transform (HHT) processing. This could be ascribed primarily to the failure of separating the correct frequency from mixed and similar frequency components. It was difficult to remove IMF signal from the earthquake record and to obtain correct earthquake energy distribution in frequency. Furthermore, The Hilbert transform sometimes induced erroneous instantaneous frequencies. Thus, care must be taken in the application of HHT in earthquake engineering. The combination of the Hilbert transform with wavelet transform could produce better analysis of earthquake record.     

A floating threshold quantization algorithm to suppressmixing interferences in partial discharge

Due to the obvious difference of energy distribution frequencies from partial discharge (PD) signal and its mixing interferences (white noise and narrow brand), we uses the characteristic that node decomposition coefficients of wavelet packet transform can effectively show the energy change of signals to build up a floating threshold quantization algorithm (FTQA) varying with the noise energy of PD decomposition coefficients. It makes the node thresholds under the optimal base various with the noise strength in decomposition coefficients to self adaptively reality the choice of optimal threshold to finely partition PD decomposition coefficients. For simulated and real PD signals with mixing interferences, the conditional global threshold quantization algorithm (GTQA) and the proposed floating threshold quantization algorithm are employed to suppress the mixing interferences in PD signals and compared, and the results show that the proposed algorithm has the stronger suppression ability to mixing interference on PD signal and keeps perfect PD waveform via suppression.     

Wavelet Analysis Methods to the Signals with Infinite Energy

We study the spectrum analysis to the signals with infinite energy using continuous wavelet transform,the concept of time-frequency power spectrum is presented,and the relations between the time-frequency power spectrum and classical power and average power are studied,the wavelet transform of self-correlation function is also presented, and the relations between it and time-frequency power spectrum are also studied.     

Binary phase only filter based watermarking combined with discrete wavelet transform

The binary phase only filter (BPOF) based digital image watermarking combined with a discrete wavelet transform (DWT) was proposed. Firstly, the DWT transform was applied to an image. Then, the discrete Fourier transform (DFT) was applied to the low frequency subband of the DWT transform. Next, the phase information of the DFT was binarized to obtain the BPOF, which would be taken as the watermark and embedded into the corresponding magnitude. Compared to applying the DFT transform to the whole image and embedding the BPOF watermark in the entire frequency range, or in the low frequency range, the watermark robustness in JPEG compression is improved significantly while maintaining the watermark imperceptibility and detection efficiency. This method may be used to demonstrate the authenticity and integrity of an image. The simulation experiments demonstrate the efficiency of this method.     

A Research on the Characteristics of Mexican-hat Mother Wavelet Used in Optic Realization

The Mexican hat mother wavelet used in optic realization is analysed. Its characteristics on time frequency domain localization, accurate reconstruction condition, regularity order and orthonormality are discussed. The error concept for the Mexican hat wavelet that the non tensor product two dimensional form of mother wavelet is obtained from the turning of its one dimensional form is corrected. The reason is explained for that the Mexican hat mother wavelet can't be used in conventional discrete wavelet transform for image data compression,but when it is used in 2 D image wavelet transform realized by optic way, it features excellent energy localization.     

A Numerical Algorithms of Fractional Fourier Transform

Signal and it's Fourier transform can reflect the info of time domain and frequence domain independently. As a usually math tool, Fourier transform is using in math, physical and engineering field widely. A new tool for signal analysis,which is named Fractional Fourier transform(FRFT), is introduced. It is interpreted in view of the classic Fourier transform. It is important to study the numerical algorithms of FRFT, because usually the FRFT can not be given to a analytical expression. A numerical algorithms of FRFT is given. It is possible to separate the distortion from the simple Gaussian signal on which a chirp distortion has been superimposed by using fractional transform.