分形插值函数反问题的小波解法

Given a graph of a fractal interpolation function f which is the attractor of an unknown IFS with affine constration maps w1 ,w2 ,… ,wN ,the maps wi(i= 1,2,… ,N)are found based on the self-similarity of the zero-crossing points of wavelet transform. The effectiveness of method is shown in an example.

波动方程的小波解法

探讨应用 Wavelet-Galerkin方法求解一维波动方程的初边值问题 ,通过修改边界上的小波函数 ,得到满足齐次边界条件的有限区域的小波基 ,用 Wavelet－ Galerkin方法离散微分方程后 ,得到一个确定小波系数的线性方程组 ,此方程组的系数矩阵在一维情况下是一个带状矩阵 ,且其中还有许多小的元素 ,其逆矩阵有类似的性质。数值实验表明，小波为求解微分方程提供了一个新的强有力的工具 ,用它来求解方程得到的小波近似解能很好地满足各种边界条件，且解的精度可以通过增加小波函数或增加尺度而得到提高。

波动偏微分方程小波解法

“波动偏微分方程边值问题”小波解法 .利用正交小波近似 ,建立 Taylor展开式逼近格式 ,对波动方程小波解法进行误差估计 ,小波解法与常规解法相比 ,逼近精度高、收敛速度快。

双曲型守恒律方程的小波解法

本文基于Hamilton-Jacobi方程的小波Galerkin近似和微分算子的小波表示,讨论一维双曲型守恒律方程初值问题的Daubechies小波解．由于小波在空间和时间上的局部性,本方法适用于处理具有奇异解的问题,可以有效的防止数值振荡．数值试验的结果表明,本方法是可行的．

边界曲线积分方程的小波解法

The boundary measure method is applied to transfer the form of the integral equation in order to use the collocation method or Galerkin method. A simple way to computer the coefficients of the wavelet series is also introduced. The way presented in this paper can be used to solve PDE problem in the two dimension region with any form of boundary.

识别变压器励磁涌流和内部短路电流的小波能量谱图解法

基于小波多分辨率分析理论,提出了一种以能量变化率的比值作为判据,区分变压器励磁涌流和内部短路电流的新方法—小波能量谱图解法。它从信号的小波能量谱图中提取特征量,作为模式识别的依据来鉴别励磁涌流和内部短路电流。仿真计算表明该方法简单有效,具有一定的应用前景。

A blind watermarking algorithm based on DWT and SVD

This paper presents a new digital image blind watermarking algorithm based on combination of discrete wavelet transform （DWT） and singular value decomposition （SVD）. First of all, we make wavelet decomposition for the original image and divide the acquired low frequency sub-band into blocks. Then we make singular value decomposition for each block and embed the watermark information in the largest singular value by quantitative method. The watermark can be extracted without the original image. The experimental results show that the algorithm has a good imperceptibility and robustness.

Application of Wavelet Decomposition to Removing Barometric and Tidal Response in Borehole Water Level

Wavelet decomposition is used to analyze barometric fluctuation and earth tidal response in borehole water level changes. We apply wavelet analysis method to the decomposition of barometric fluctuation and earth tidal response into several temporal series in different frequency ranges. Barometric and tidal coefficients in different frequency ranges are computed with least squares method to remove barometric and tidal response. Comparing this method with general linear regression analysis method, we find wavelet analysis method can efficiently remove barometric and earth tidal response in borehole water level. Wavelet analysis method is based on wave theory and vibration theories. It not only considers the frequency characteristic of the observed data but also the temporal characteristic, and it can get barometric and tidal coefficients in different frequency ranges. This method has definite physical meaning.

Vibration-based feature extraction of determining dynamic characteristic for engine block low vibration design

In order to maintain vibration performances within the limits of the design, a vibration-based feature extraction method for dynamic characteristic using empirical mode decomposition （EMD） and wavelet analysis was proposed. The proposed method was verified experimentally and numerically by implementing the scheme on engine block. In the implementation process, the following steps were identified to be important： 1） EMD technique in order to solve the feature extraction of vibration signals; 2） Vibration measurement for the purpose of confirming the structural weak regions of engine block in experiment; 3） Finite element modeling for the purpose of determining dynamic characteristic in time region and frequency region to affirm the comparability of response character corresponding to improvement schemes; 4） Adopting a feature index oflMF for structural improvement based on EMD and wavelet analysis. The obtained results show that IMF of signal is more sensitive to response character corresponding to improvement schemes. Finally, examination of the results confirms that the proposed vibration-based feature extraction method is very robust, and focuses on the relative merits of modification and full-scale structural optimization of engine, together with the creation of new low-vibration designs.

Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets

In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.

Wavelet matrix transform for time-series similarity measurement

A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet subspace,and sample feature vector and orthogonal basics of sample time-series sequences were obtained by K-L transform. Then the inner product transform was carried out to project analyzed time-series sequence into orthogonal basics to gain analyzed feature vectors. The similarity was calculated between sample feature vector and analyzed feature vector by the Euclid distance. Taking fault wave of power electronic devices for example,the experimental results show that the proposed method has low dimension of feature vector,the anti-noise ability of proposed method is 30 times as large as that of plain wavelet method,the sensitivity of proposed method is 1/3 as large as that of plain wavelet method,and the accuracy of proposed method is higher than that of the wavelet singular value decomposition method. The proposed method can be applied in similarity matching and indexing for lager time series databases.

Wavelet solutions of Burgers' equation with high Reynolds numbers

A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.

Application of Wavelet Transform Modulus Maxima in Raman Distributed Temperature Sensors

We proposed and demonstrated a wavelet transform modulus maxima （WTMM） de-noising method to decrease the temperature error. In this scheme, the composition scale was determined simply by the WTMM amplitude variation with the growth of the decomposition scale at 30 ℃, and the signal WTMM was obtained by the wavelet decomposition modulus on every decomposition scale based on the modulus propagating difference between the signal and noise. Then, we reconstructed the signal using the signal WTMM. Experimental results show that the proposed method is effective for de-noising, allowing for a temperature error decrease of about 1 ℃ at 40 ℃ and 50℃ comparing to the original data.

Detection and identification of S1 and S2 heart sounds using wavelet decomposition method

Phonocardiogram （PCG）, the digital recording of heart sounds is becoming increasingly popular as a primary detection system for diagnosing heart disorders and it is relatively inexpensive. Electrocardiogram （ECG） is used during the PCG in order to identify the systolic and diastolic parts manually. In this study a heart sound segmentation algorithm has been developed which separates the heart sound signal into these parts automa- tically. This study was carried out on 100 patients with normal and abnormal heart sounds. The algorithm uses discrete wavelet decomposition and reconstruction to pro- duce PCG intensity envelopes and separates that into four parts： the first heart sound, the systolic period, the second heart sound and the diastolic period. The performance of the algorithm has been evaluated using 14,000 cardiac periods from 100 digital PCG recordings, including normal and abnormal heart sounds. In tests, the algorithm was over93% correct in detecting the first and second heart sounds. The presented automatic seg- mentation Mgorithm using w^velet decomposition and reconstruction to select suitable frequency band for envelope calculations has been found to be effective to segment PCG signals into four parts without using an ECG.