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.     

Pulse Signal Analysis of Druggers with the Wavelet and Neural Network

The most significant difference between the human pulse signals collected from heroin druggers and healthy persons is at their amplitude waveforms as time functions. That is, the amplitude values and change rates of two types of signals, within a particular time range, appear different features. However, the partial components of the scaling and wavelet coefficients of the pulse signals obtained by using wavelet transform can reveal such key features. The pulse signals of 15 heroin druggers and 15 healthy persons are analyzed through using the muhiresolution analysis of wavelet transform. By using db2 orthogonal wavelet, every pulse signal is decomposed into three levels and the absolute values of the sixth component of scaling coefficients and the second component of the wavelet coefficients in the third level are combined to form a feature vector. A probabilistic neural network with good detection performance is successfully designed for automatically detecting 30 feature vectors. During the network design, 20 feature vectors are used as training samples. The remained 10 feature vectors are used as testing samples. Based on these steps, 15 heroin druggers and 15 healthy persons are all correctly identified. In other words, the detection rate arrives at 100%. druggers.     

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.     

Independent component analysis and its application in estimating VEP

Original signals can be effectively estimated from their linear mixed signals by independent component analysis (ICA), even though their frequency components are overlapped, which provides a way to estimate the faint electrophysiological signals. And many researchers who study biomedical signal processing have paid great attention to the technique. We discuss the ICA model and the implement of a fixed-point fast ICA algorithm based on negentropy criterion. With the algorithm, we availably pick up the simulated visual evoked potential (VEP) from the mixing signals.     

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.     

Parameter optimized Morlet wavelet de noising method based on cross validation method

A new de noising method based on parameter optimized Morlet wavelet is put forward. The Morlet wavelet is chosen as the mother wavelet because its shape is similar to the mechanical shock signals. The mother Morlet wavelet is improved by adding two parameters which decide the shape of the mother wavelet in time domain. The added parameters and the appropriate scale parameter for the wavelet transformation are designed by the cross validation method. Finally, the useful components of the signal can be obtained by the improved Morlet wavelet de noising method. The gear fault diagnosis experimental result shows that the proposed method has a good de nosing performance and it is effective in fault feature extraction.     

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.     

Hilbert-Huang transform and denoising for partial discharge ultrsonic singals of large motor

Empirical mode decomposition (EMD) algorithm is introduded as the core of the Hilbert-huang transform (HHT), and implementation process of EMD is analyzed. Then data compression denoising algorithm based on EMD is proposed, simulation and experimental signals are used for verification of the effect of EMD. In the same data sources, the comparison of data compression denoising approaches based on the EMD, db2 wavelet and db8 wavelet are conducted. In addition, physical experiment of the same analysis and comparisons are conducted on a running motor in a Chongqing electrical plant. Simulation and experimental results show that data compression denoising algorithm based on EMD can achieve the same denoising effect, or even better than based on db2 wavelet, db8 wavelet. The former is more perfect than the latter in the real signal processing, and denoising based on EMD is not loss of the original signal energy.     

Based on Wavelet Transform to Extract and Analyze Rabbit Somatosensory Evoked Potential

To extract rabbit somatosensory evoked potential(SEP),the authors locate waveform of rabbit SEP and analyze it.The rabbit was narcotized and stimulated by 0.5 Hz electric pulse.Potential of scalp was sampled at 3 764 Hz.Rabbit somatosensory evoked potential was extracted by one-dimension multi-resolution analysis,and continuous wavelet transform(CWT) was employed to locate and analyze the wave of SEP.The results show that Single-trail SEP can be extracted by Daubechies wavelet,when compared wavelet transform result of single-trail with result of averaged SEP.Wave component of SEP can be located precisely through the method of continuous wavelet transform.Frequency feature of SEP can also be analyzed by CWT.The technique of continuous wavelet transform,which can project a one-dimension signal into a two-dimension time-frequency space,will become a useful method to process medical electronic signal.     

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.     

R-factor Pseudo-circular Extension Method

The extension methods of finite length signals for sub band coding associated with wavelet transformation are investigated.Considering the weakness of the existing extension methods,an extension method is presented which is named r factor pseudo circular extension method.It turns out theoretically that the input signal can be reconstructed exactly from the truncated section of the analyzed signals by our method and the method is better than other existing extension methods,as shown in many examples.A new valid way is provided for wavelet transform application in data compression.     

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.     

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.     

Effective Coefficient Threshold for Complex Wavelet Transform

This paper constructs complex wavelet which used for suppressing white noise in PD,and then analyses some disadvantages of several existing wavelet threshold and presents a method of Effective Wavelet Coefficient(EWC) according to the characteristic of modulus maximum of PD signals.Then it is compared with maximin theory threshold selection and Stein unbiased risk estimate theory threshold selection.The findings suggest that the method of EWC is adaptive,and it can suppress noise completely with small distortion of PD signal.     

Detecting EEG Sleep Spindles by Digital Filtering with Zero Phase Error

EEG signal is a kind of very complex non stationary signal. It is of important clinical values for using EEG most efficiently to distinguish all kinds of components in EEG or getting needed components to judge some pathology features effectively. The phase moving of the system can change the relative phase relation between the components in the inputed signal, so there can be a great change of the feature in time domain of inputed signal. The FRR and RRF digital filtering methods and their realization are discussed. By using these methods, the system can be of the feature of zero phase error, and the filtering of EEG signals with zero phase error can be realized. Based on the definition of sleep spindles, we can detect sleep spindles in time domain directly by using digital filtering with zero phase error.     

Real time monitoring for multivariate statistical process with on line multiscale filtering

By analyzing shortages of current MSPCA model, an on line multi variable statistical process monitoring method is proposed, which uses some concepts from online multi scale filtering and can be applied to sensor fault diagnosis. In the method, wavelet decomposition is employed to the signals using edge correction filter in a fixed length data window, and then wavelet denoising is conducted with wavelet threshold filtering. Next, an on line multi scale model is constructed for data combining wavelet transformation and adaptive PCA in the previous data window. This model avoids time waste in direct signal denoising and reduces time cost in multi scale data with conventional PCA, which eventually increases accuracy in fault diagnosis. Experiments on eight vibration signals of 6135D diesel engine under severe leak condition prove the practicability and feasibility of the proposed method.     

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.     

A Wavelet Function Generator Using Switched Capacitor Filter

A wavelet function generator making u se of the characteristics of switched capacitor filter is constructed,it can produce anveniently the waveforms of wavelet signals in different scales.A concrete practical scheme is also proposed.The mean square error between practical signal and theoretical signal can be made as small as possible so long as the number of samples is large enough and sample duration is small enough.     

Systems Analysis Based on Continuous Wavelet Transform

The linear time invariant vibration system is analyzed by Continuous Wavelet Transform(CWT),the relationship of wavelet transform of output signal with the pulse response of system and input signal is put forward.As an exapmle,the wavelet transform of the output signal of system with single degree of freedom is calculated and compared with the direct wavelet transform result of the actual output signal,it shows that the two results are in complete agreement.     

Suppression of Periodic Narrowband Interferences in Cable Partial Discharge Detections

There are background noises and interferences in the signal acquired,due to partial discharge(PD) detection system covers a broad frequency band.To suppress periodic narrowband signal which is a quite serious interference in PD measurement,the existing suppression method is introduced,the new method of wavelet packet transform is mainly studied to de-noise the periodic narrowband in XLPE cable PD detection system,which is based on the db4 basic wavelet using soft threshold.The results of the experiment show that wavelet packet transform is effective in restraining the periodic narrowband interferences to extract the PD pulses in XLPE cable PD monitoring system.