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On the basis of the definition of the extraordinary Radon transform, the theory of rebuilding image from extraordinary Radon transform result is proposed, and some category such as image structure notation, topology of image structure notation and topological space, homeomorphism in topological space, equivalence of homeomorphism relation, topological constant of image structure notation.

与现有的基于区域内部或外形变换的形状分析方法相比，在理论方法上本质不同的是，本文提出的广义Radon变换，直接将原始的图象数据影射到特征空间，给出图象构图特征的描述，给出了可以用来进行图象检索或图象识别的结构特征谱。

The commonly used real time detecting theory of instaneous reactive and harmonic current based on vector transform has the shortcomings of complexity of vector transform and illegibility of physics meanings.

针对建立在瞬时无功功率理论的基础上的瞬时无功和谐波电流检测算法存在的矢量变换复杂，物理意义不明确的缺陷。

In the data acquisition system, CD4051 and AD574- the A/D transform, are used as hard core to receive the signal from the infra-red ray temperature sensor; the data acquisition depend on CPU; in the keyboard/ display system, a 74LS48 as the driver to drive LED works; in the warning circuit, I used two color LED and a buzzer as one unit to work; DAC0832 converter is the center of the D/A transform; execution unit, I used DDZIII type electromotive unit; the auto-man, it is a disabling of the other control circuit, this can secure production all the time.

在数据采集部分，以多路开关CD4051和AD574模/数转换器为核心接收来自红外线传感器的信号；数据处理依赖CPU；键盘/显示部分，以74LS48驱动LED数码管工作；报警单元，采用了双色LED加蜂鸣器的组合；D/A转换采用了DAC0832转换器；执行器采用DDZIII型电动执行器；手/自动切换装置则屏蔽了之前的电器部分，安全可靠。

Combining with discrete wavelet transform, the integral wavelet transform has been realized on hardware system, and the experimental results are satisfying.

同时结合离散整数小波变换算法，在硬件系统上实现了整数小波变换，取得了较好的试验效果。

The fundamental solutions are obtained by Hankel integral transform and numerical inverse transform.

采用Hankel变换及数值逆变换得到饱和土的基本解。

The digital algorithms of integral and discrete wavelet transform are presented for purpose of electric power system protection, based on the analysis of wavelet transform for sampled digital signals under the Shannon sampling theorem.

从电力系统继电保护应用的角度，结合香农采样定理，深入探讨了连续信号和离散信号的小波变换的关系，给出了离散信号的积分小波变换和离散小波变换的数字计算方法。从理论上研究了信号小波变换的误差与尺度函数和小波函数的关系。

The current signals were gathered in the tests, and processed by wavelet package transform. A characteristic vector was constructed by the energy of different frequency segment, which was calculated by using the coefficient of wavelet package transform of the current signals. The vector shows that the energy of low frequency segment is of the majority of the total energy, and becomes larger as the interelectrode gap decreasing.

在线采集真实电解加工过程中的电流信号，用对实测信号进行小波包分解和重构后的小波系数计算各频段的能量，构造一个由不同频段能量组成的特征向量，发现特征向量的低频分量占总能量的大部分，随着平衡间隙的减小，低频分量能量增大。

Owing to the approximate and detail coefficients at each level after decomposition using undecimated wavelet transform have the same length as the original signal, the transform can possess time invariant property and retain more characteristics in time domain, and therefore improve the effect of denoising.

由于非降采样小波分解后的各层系数和原始信号的长度均相同，因此在具备平移不变性的同时还能保留更多的时域信息，从而可以提高信号的降噪效果。

The kernel requarment for the rotating invariant property of a TFD based on fractional Fourier transform is proposed and proved in chapter 5. A close formula of Radon-Wigner transform of LFM signalis given. Based on the formula, the distribution of RWT is discussed.

第五章在首先简单介绍分数阶付立叶变换的基础上，提出并证明时—频分布具有旋转不变性对核函数的要求，给出了Radon-Wigner变换在直角坐标系下分布的一个显式公式，据此讨论了RWT分布特点。

This procedure according to the formula to achieve the inverse discrete cosine transform, you can write your own validation of discrete cosine transform is correct, understanding the formula help.

详细说明：这个程序根据公式实现了离散余弦逆变换，可以验证自己编写的离散余弦变换是否正确，对理解公式有帮助。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。