General Construct Method & Software of Wavelet Base's Filter

Wavelet analyses have been used for many fields deeply, especially , the wavelet transforms on compact support sets have been applied to signal dealing and image compression etc. However, the constructing of wavelet base is a hard work to do. In this paper, for N=2k the analysis structure of wavelet base on compact support sets are found successful. That is the general solutions structure of equations which fits to the wavelet base orthogonal conditions, Those formulas or algorithms make it very easily construct many filters of wavelet base, at the same time , Daubechies's filters and some other filters which are important in apllications have been tested correct; With the aid of our formulas , it is very easy to dynamically choose the wavelet bases.     

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.     

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.     

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.     

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.     

Two Channel Filter Banks and Wavelet Transform of Discrete Sequences

Multirate filter banks and wavelet transform are closely related theoretically and practically. This paper researches the wavelet transform of discrete-time sequences basing on dendriform filer banks in the signal processing field, analyses the theory and design method of two channel conjugate quadrature mirror filter banks and fast implement of discrete orthogonal wavelet transform and generation of orthogonal wavelets, and points out the internal relationship between them.     

Denoise Based On Translation Invariance Wavelet TransformAnd Its Applications

De_noising algorithm based on traditional wavelet transform may produce artifacts on discontinuities of the signal. The reason is that the de_noising algorithm lacks of wavelet translation invariant. This paper proposes a de_noising method based on translation invariant. The method performs the cycle_spinning for the signal to be analyzed. And then, the soft (hard) thresholding is used to shrink the wavelet coefficient of the signal and reconstruct the signal. Consequently, the shift dependence of wavelet basis is eliminated. This method can suppress the artifacts effectively so that de_noised signal is more smooth and has better approximation to original signal.     

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.     

Better subcarrier bases for powerline communication system

To solve the frequency dispersive feature in powerline channel, the quthors analyzed the anti-interference performance of modulation schemes with different subcarrier bases, and use orthogonal wavelet packet as subcarrier base instead of sine base in OFDM to suppress multi-path effect and frequency selective fading by its orthogonality in powerline channel. Through experiment, performances of wavelet packet modulation with different wavelet packets and OFDM are analyzed. Experiment results indicate that when the SNR has reached a certain level, orthogonal wavelet packet modulation has better performance than bi-orthogonal wavelet packet and sine base.     

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.     

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.     

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.     

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.     

A Practical Method of Eliminating the White Noise of Partial Discharge with Wavelet

The white noise of PD(partial discharge) signal brings great difficult to the PD signal's processing, so eliminating the white noise is a necessary section. There are many methods of eliminating white noise, but none of them are suitable to the PD signal processing. Because PD signal and white noise have different Lipschitz exponents and different wavelet transform features in time-scales, a new eliminating white noise method has been brought forward that has simple operation and meets the timing need of PD signal's processing. After the processing with this method, the PD signal is not distortion and the effect of eliminating white noise is very good. This method can be applied to the processing of PD signal gotten from the site.     

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.     

Detection Method for R-Wave of ECG Signal With Wavelet Transform

The R-wave of ECG signal represents the electrical activation of the ventricles, which initiates ventricle contraction, and the typical peak value singular signal, so the R-wave of ECG signal is localized precisely and analyzed accurately using the wavelet transform. The principium of the precise detection method for R-wave in ECG signal is researched. The special properties of Mexican hat wavelet in time-domain are analyzed, too. This wavelet has every order continuity, symmetry, exponential attenuation and one vanishing moment. For this reason, the mexican hat wavelet basis has the excellent localization and analyzing precision. Using the MIT/BIH (Massachusetts Institute of Technology / Boston's Beth Israel Hospital) Arrhythmia Database and the applications in clinic, the precise detection method can detect accurately and localize precisely to the R-wave in ECG signal in the serious noise signal. This method has the quite high locating precision (its error is not more than one sampling point and the points of the R-wave in ECG signal about 80 percent are localized precisely) and analyzing accuracy (no accumulative error). The real-time of the method is excellent, and the real-time detection to the R-wave of ECG signal can achieve using this method.     

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.     

Time-frequency Analysis of Heart Sound

The structural defects of the heart are often reflected in the sounds that heart produces. Because of the non-stationary of the PCG signal, it is important to maintain its time-frequency character. We discuss the Short-Time Fourier Transform (STFT) method and the wavelet method. Some normal and abnormal heart sounds were analyzed by these methods. We can see the advantage and disadvantage of them obviously from the examples.     

Wavelet Neural Network Equalizer Using Error Feedback Structure and Algorithm

The inter-symbol interference in the nonlinear time-varying channel is a serious problem in the wireless communication. In order to overcome it, wavelet neural network equalizer using error feedback is employed to cut the auto-correlation of the error signal. Exploiting the decent time-frequency localization of the wavelet analysis, as well as the self-training feature of the neural network, a quicker convergent nalysis and computer simulation confirm the effectiveness of the equalizer and a lower BER are attained. Theoretical aalgorithm. It at The wavelet neural network equalizer based on error feedback advances the communication in the nonlinear time-varying channel.     

Detecting a fault line under a single phase to ground of distribution network based on analysis of multi frequency bands

Addressing the problem of choosing a fault line under single phase to ground of distribution network, we presented a new criterion based on analysis of the development of fault line selection and a method using wavelet packets. The feature frequency band, or the combined feature frequency bands of each line, in which the transient capacity current was concentrated was chosen for maximum energy. Based on the principle that the transient capacity current's energy of the fault line was larger than the that of normal lines, fault line selection can be carried out adaptively by contrasting the energy of the transient capacity currents of all lines in each chosen frequency band. The simulation results and spot testing data shows the proposed method can detect the fault line in distribution networks precisely and reliably.