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.     

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.     

A Vector Quantification Image Coding Scheme Based on Wavelet Transform

The paper proposes an image compression and coding scheme based on discrete wavelet transform (DWT), which makes the best of the relativities among original image and coefficients of wavelet, the relativities among pixels of subimages, the relativities among directions of subimages. Human visual specialities were considered, so the compression scheme leads up to make full use of the statistical redundancy and visual redundancy of image. To get high compression ratio and good quality of image, the coefficients of image working on the quality of image greatly were reserved accurately, but the coefficients of image working on the quality of image slightly were quantified roughly. Also, the regrouping and coding of the coefficients could be used universally. The experimental results show that the compression method is provided with simply calculating, little time for coding and decoding and satisfying quality companied with high compression ratio.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Wavelet-Based Multiresolution Analysis to Noise Elimination

The wavelet transform is a new subject developed quickly in the past ten years Compared with Fourier transform and Gabor transform, the wavelet transform is a part of time-frequency transform, so the message can be obtained from the signals effectively. By means of the fractionized multiresolution analysis to the signals, many problems unalbe to be solved by Fourier tranform have been solved in this way.Based on the fact that the maxima of the noise wavelet transform reduces dramatically with the increase of the scale, we obtain the result that this way is more advanced than the Fourier transform multiresolution analysis to the noise elimination.     

A New Solution to Reduce Blocking Artifacts Introduced by Standard Fractal Methods

Fractal image coding techniques usually partition the input image into small range blocks. This artificially introduces boundaries into the image resulting in the unpleasant blocking artifacts in the decoded images especially at high compression rate. Because the effect is especially responsible for the restrictions of the block-based coders, the solutions must be sought to reduce this blockiness. Recently two possible schemes have been proposed by other researchers: One may try to use overlapping blocks in the fractal transform, and the other to employ the combined fractal wavelet approach. An alternative solution is proposed, which employs the bilinear interpolation techniques and the resolution independence of fractal coding, in the sense that an image can be decoded at higher or lower resolutions than the original. Experiments show that the proposed scheme can eliminate the blocking artifacts.     

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.     

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.     

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.     

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.     

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.     

Application of higher density wavelet transform to composite fault diagnosis of rolling bearing

Aiming at the difficulties in accurate reorganization of several weak faults currently, a composite fault diagnosis method based on higher density discrete wavelet transform and envelope spectrum is proposed. Firstly, the higher density discrete wavelet transform is used to decompose acquired vibration signals of rolling bearings. Then, the single-subband reconstruction is performed on the wavelet coefficients and scaling coefficients at each scale in order to solve frequency aliasing. Finally, the envelope spectra of all subband signals are calculated, and all faults can be recognized according to the characteristic frequencies of the typical faults. The proposed method is applied to the diagnosis of the rolling bearings with composite faults, and is compared with other common fault diagnosis method. The results show that the proposed method can be effectively used for the early composite fault diagnosis of rolling bearings.     

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.     

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.