查询词典 wavelets

First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

Firstly, after getting predicted multiples, we use adaptive subtraction algorithm to eliminate multiples and get some inverse wavelets corresponding to every trace in one shot gather, then construct inverse wavelets domain by those inverse wavelets. Secondly, use median filtering method to get inverse wavelet estimation in inverse domain. Thirdly, correct the misshaped inverse wavelets in inverse domain by the inverse wavelet estimation.

其步骤为：首先用SRMA方法预测出表面多次波，并对每一单炮进行单道自适应相减，得到逆子波，形成逆子波域；其次，在逆子波域采用中值滤波，提取接近真实逆子波的逆子波估计；第三，在逆子波域用逆子波估计对畸变的逆子波进行校正；最后采用校正后的逆子波来衰减多次波。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

These new wavelets inherit some basic properties of the corresponding classical wavelets, such as the orthonormality, the order of regularity, the time-frequency localization characteristics, and so on, meanwhile some performances of the new wavelets are improved.

新子波类中的每一个子波均继承了原始子波的许多基本性质，比如规范正交性，正则阶，时、频局域化特性等，同时也得到某些性能的改善。

Finally, we prolongate the theory to two dimension tensor product wavelets space, proofing the best approximation property of product spline wavelets interpolation and constructing the parallel algorithm of the wavelets decomposition.

最后，我们继续将这一理论拓展到二维张量积小波空间，验证了乘积型样条小波插值的最佳逼近性质，进而在二维张量积小波空间构造了乘积型样条小波分解的并行算法。

With fault signals of vibration tested in practice, this paper takes frequency-domain half-power bandwidth Gauss wavelets of continuity, index wavelets decomposition and equivalent bandwidth equivalent sampling discrete bi-orthogonal wavelets decomposition as basis, presents scaling correlated analysis correspondingly toward wave making vibration signals, and accurately realizes to decompose different stress wave speeds, and provides a method of analysis and calculation for accurated location and recognition of the polygenetic faults.

根据上述故障力学模型，我们提出并设计了相应的测试系统，对实测的故障振动信号，以频域半功率带宽连续高斯小波、指数小波分解和等带宽等采样离散双正交小波分解为基础，提出了相应的对波致振动信号的尺度相关分析，准确地实现了分离不同的应力波速，为多源故障的精确定位识别提供了分析和计算方法。

The issues of present seismic wavelet frequency caused by different concepts, such as apparent frequency, dominant frequency, peak frequency and centroid frequency, etc., which are defined by different methods, and understanding deviation, definition of seismic wavelet frequency for time and frequency domain are concluded and summarized. On this basis, three kinds of seismic wavelets in common use such as Ricker and Zinc wavelets as well as sine wavelet with exponential attenuation characteristics are analyzed and a conclude is achieved that apparent frequency and dominant frequency are consistent in essence, but peak frequency and centroid frequency as well as apparent frequency or dominant frequency are not completely consistent with different seismic wavelets. For actual seismic data, peak frequency can approximately be used as dominant frequency, but it is not suitable when seismic wavelet is known for it can give out any wrong knowledge and results.

针对目前地震子波频率由于定义方式出现的各种概念（视频率、主频、峰值频率、中心频率等）以及理解上出现的偏差等问题，首先从时间域定义和频率域定义2个方面进行了归纳和总结，并在此基础上对3种常用地震子波（Ricker子波，Zinc子波，正弦指数衰减子波）进行了分析和研究，得出视频率与主频概念一致，但不同地震子波的峰值频率、中心频率和视频率之间并不完全一致的结论；而对于实际地震资料，将峰值频率近似看作地震子波的主频是可以的，但在地震子波已知的情形下这样做是不恰当的，甚至可能会得出错误的结论和认识。

Inspired by the wavelets,we introduce the concept of geometric wavelets.We transform the compression into a best uniform approximation which is familiar to us in mathematic,we approximate the signal with polynomials.

受小波方法的启发，我们引入了几何小波的概念，将压缩问题转化为逼近理论中熟知的最佳一致逼近问题。

We fould that most reconstruction algorithm based on wavelets did not consider about the noise. And so, we proposed the denoised reconstruction algorithm based on seperable MRA, in which added regularizion denoised method based on wavelets.

发现大多数小波重建算法都没有对图像的噪声进行处理，基于此，提出了对基于可分离MRA的小波去噪重建算法，融入了基于小波的阀值化去噪算法。

A technique based on lifting scheme is presented to construct the compactly supported wavelets whose coefficients are composed of a free variable. When t=1, the integer wavelets based on lifting scheme only use integral addition and shift, so it's fast and easily realized via hardware.

在理论上，基于提升理论构造了一种包含自由变量t的紧支撑小波，选取参数t=1的9/7整数小波基，只需要整数加法和移位实现，运算量低，便于硬件实现。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。