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.     

Application of Wavelet Transform and HMM Model in Recognition of Speech Signals

Some parameters based on wavelet transform and ARMA Model are presented. Wavelet transform provides a high frequency resolution, and the ARMA model is more powerful due to its including of the zeros pole in the model. The experimental result of alphabet of A to N from National Institute of Standard Technology (NIST) database is given. The error rate has been improved, especially C.     

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.     

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.     

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.     

Realizing Continuous Wavelet Transform with linear Analog filter

A method of realizing wavelet transform with linear analog filter is proposed. It shows another new way of obtaining fast wavelet transform. It has also given out a procedure of constructing such a filter network and verified by the Mexican hat Wavelet.     

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.     

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.     

Study on Wavelet Analysis of Impact echo Signal

Based on the characteristic of the continuous wavelet transform for the impact echo signal,the wavefronts of longitudinal waves and transversal waves in the impact echo signal can be estimated precisely,and it is improved that the precision of the dynamic elastic properties of materials evaluated through impact echo.     

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.     

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.     

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.     

A Simplified Denoising Algorithm with Wavelet Transform

This article explains the mathematical characterization of singularities with Lipschitz exponents and how to compute Lipschitz exponents.The principle and advantage of denoising with wavelet are reviewed.At last,a new simplified practical denoising algorithm is given.     

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.     

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.     

Wavelet Analysis in the Signal Processing

The conceptions of mother wavelet and complete wavelet system are introtuced.Their digital features are described in detail.The definitions of con ti n nons, discrete, and dyadic discrete wavelet transforms are given,and their inverse transforms are deduced with reference to thevector expressions in R2 space.     

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.     

VBR Coding Algorithm Based on Wavelet Transform

The introduction of the asynchronous transfer mode(ATM) concept has significantly influenced the coding theory.According to the characteristics of the ATM network,using the advantages based on the wavelet transform,how to apply the wavelet transform to plane separation and how to apply VBR coding to the layered data are discussed.The results of experiment are described respectively.     

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.