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.     

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.     

Filter Design of Wavelet Transform for 2-D Image

The filter design is the key to 2-D image wavelet transform. Based on the studying of image properties and 1-D wavelet theory,the authors describe a parasymmetry boundary extension method and realize 2-D discrete wavelet transform by means of 1-D wavelet transform according to correlation of adjacent pixels. Also,it is proved that the discrete wavelet transform of inverse data stream in row and the sign of discrete detail signal will be inversed,and that a filter of wavelet transform based on symmetry of bi_orthogonal filter is constructed. The test has proved the fine reconstruction and perfect SNR.     

Time-frequency Characteristic of Wavelet Base and Its Application Transient Signal Detection

The application of wavelet analysis in fault diagnosis is growing rapidly.There are many different wavelet base to use but no accepted procedure for choosing among them, the analysis results by using them have great difference. This paper describes the significant properties of wavelet base, and analysis behavior of transient signal in wavelet transform, result on some methods for how to choose wavelet base in analysis transient signal.     

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.     

Choosing Method of Wavelet Neuron Based on ECG Data Compression

The paper discusses a wavelet network for the ECG data compression and proposes the method for choosing its wavelet neuron.According to the spectrum range of the ECG data,we decide the time-frequency field of ECG.And the time-frequency field of wavelet is also determined by the spectrum range of it.The wavelet neuron is fixed preliminarily by the first two steps.Then the preliminary wavelet neuron is screened by using OLS algorithm.We choose Morlet as the mother wavelet,and use the ECG signal to validate by the method.The result demonstrates that the number of Morlet whose spectrums locate at the ECG's is up to 152.But after screening by the OLS algorithm,it reduces sharply.This method can make the size of the wavelet network driving to optimum and also reduce the training time of the wavelet network sharply.     

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.     

Computation of the Wavelet and Scaling Functions Using Coefficients of Wavelet Filter

To associate the discrete wavelet transform with the continuous wavelet transform, an iterative convolution algorithm is given by analyzing the and scaling function using coefficients of wavelet filter. usually used methods of the computation The way of judging the convergence of improved algorithm on of the wavelet function iterative convolution is given. The advantages of improved algorithm is analyzed. The experimental result shows that the modified algorithm is effective.     

PD Pattern Recognition Using Complex Wavelet Transform Coefficient As The Feature

Complex wavelet transform can characterize the partial feature of the PD signal in time-domain and frequency-domain,and provides the unique phasic information.In this paper,the PD pulse waveforms which are created by 4 typical insulated defects are transformed by complex wavelet,and then the complex wavelet coefficient's real part,imaginary part and compound coefficient are clustered by the Fuzzy c-means,the energy of the cluster is the feature of pattern recognition.Discharge samples are got through large number of experiments,and BPNN can identify the PD created by 4 typical insulated defects effectively.The results show that the feature extracted from compound coefficient is better than the feature extracted form the real part and imaginary part of complex wavelet coefficient or wavelet coefficient.     

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.     

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.     

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.     

Construction of Orthogonal Wavelets Bases and Design of Algoritm

Based on the brief introduction of the principle of wavelet analysis,a summary of several typical wavelet bases from the point of view of perfect reconstruction of an image is given.It is emphasized that designing wavelet bases which are used to decompose the image into sub band form is equivalent to designing a fliters with perfect or nearly perfect property.The generating algorithm corresponding to Daubechies bases and some simulation results are also show in this paper.     

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.     

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.     

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.     

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.     

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.     

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.     

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.