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Using the limit definition of Fourier transform, the paper has proved the universal form of Fourier transform differential and integral characteristic theorem, explained its application method, and pointed out that errors can be substantially reduced by using this method.

提要：本文采用Fourier变换的极限定义式，证明了普遍形式的Fourier变换微积特性定理。

This paper is composed of the algorithm design of dual-tree binary coefficients complex wavelets,MGM algorithm for linear systems that can be diagonalized by generalized discrete Fourier transform and type-II discrete sine transform matrices, wavelet and MGM algorithms for Toeplitz systems and their applications in signal and image processing.

本文以多进制小波与对偶树二进制系数复数小波算法设计、三角变换对角化系统MGM算法、Topelitz系统的小波与MGM结合算法作为理论主线，以对偶树复数小波与扩散方程方法结合的图像去噪，信号与恢复作为应用背景展开讨论。

In compare to Fourier transform, wavelet transform is a local one both in time and frequency domain.

与傅立叶变换相比，小波变换是一个时间和频率的局域变换。

Fractional Hilbert transform, a generalization of Hilbert transform from integral order to fractional order, extends the application fields.

基于广义Hilbert变换将传统的Hilbert变换由整数阶向分数阶的推广，其应用领域也得到了扩展。

The blind digital watermarking algorithm based on Fresnel diffraction transform, phase encryption mask and discrete wavelet transform is proposed.

基于菲涅耳衍射变换和相位密码板，结合离散小波变换，设计了一种新的盲数字水印算法。

Because the transform matrix calculated with the Fresnel integral was non-unitary,YG algorithm was used to design the DOE realizing beam shaping in the fractional Fourier transform domain in this paper.

鉴于该变换矩阵非幺正，本文利用YG算法进行了光束整形器件的设计。

Since CGH is not real-time available,many scholars are studying the real-time applications of CGH with modern display devices, such as liquid crystal display, The applications include, real-time pattern recognition using liquid crystal display based joint transform correlator, CGH interferometric technology for anti-counterfeiting, and real-time application of Furrier transform CGH.

但由于存在不能实时实现的弱点，许多学者用现代显示器件进行了计算全息实时应用研究，如：光学联合变换滤波器图像识别技术，实时计算全息干涉防伪技术，傅里叶变换实时全息图应用。

All the algorithms referred hereinbefore are implemented through experiments and compared with traditional separable wavelet transform to demonstrate the effectiveness and superiority of contourlet transform for image processing.

以上算法都通过实验与传统可分小波变换的图像处理结果作对比以证实Contourlet变换在图像处理中的有效性和优越性。

A filter of capillary electrophoresis signals with online wavelet transform was developed. The online wavelet transform with fixed time window was used and how to select the hest length of time window was discussed.

将在线小波变换用于毛细管电泳信号的滤噪处理，满足了毛细管电泳信号采集过程中实时处理和监控的需求。

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 operators will suffer a temporary decrease in the number of consumers and short message services as people may not like having to provide their ID cards for a phone number," Xu Junqi, vice-dean with the Policy-Making Institute of the Telecommunications Research Centre under MII, said yesterday.

信息产业部下属的通信决策研究院副主任徐俊其昨天说：&实行手机实名制后，人们可能不太情愿用身份证注册手机号，所以通信运营商会暂时面临用户减少和短信用户减少的问题。&

I don't believe in make-believe!

我不相信这些虚构的故事。