变换

Chapter 3 introduces some methods seeking exact solutions for the nonlinear evolution equation, such as inverse scattering method, symmetry reduction method, Backlund transformation, Darboux transformation , Hirota bilinear method, Painleve analysis method, AC = BD model, and so on.

第三章简要介绍了非线性发展方程的若干求解方法，如反散射方法，对称与微分方程约化，Backlund变换和Darboux变换方法，Hirota双线性方法，Painleve奇性分析法，AC=BD框架下的精确求解等。

This conclusion can also be proved by spectrum-warping audio watermarking algorithm in MCLT domain. To discuss further deeply on why spectrum-warping technique does not have the required robustness, the studies are carried out upon the essentials of bilinear transformation. All the theoretical analysis and experiments results put the robustness of the spectrum-warping audio watermarking under questioning.

四、提出了基于量化的变换域音频水印算法中关于量化参数的选择方法量化变换系数的音频水印算法是以修改谱分量幅值为基础，算法的主要问题是如何选择量化参数以确保算法的鲁棒性和不可感知性，另外量化系数的区域选择也会影响算法的性能。

We proposed the simplest structure of 2-D bilinear transformation digital circuit, we proposed four approaches of the realizations:(1) Realization of 2-D discrete domain difference equations;(2) 2-D FFT realization;(3) Digital hardware implementation;(4) by 2-D recursive digital structure to realize them.

在第七章，我们则重点研究了二维数字滤波器的实现问题。我们对第六章提出的2-D双线性变换电路又作了进一步的简化，获得了一种最简结构的二维双线性变换数字电路，该电路仅有二个延时器和一个乘法器。在第七章里，我们提出了二维跳耦型数字滤波器的四种实现方法：(1)二维时域差分方程实现；(2)二维FFT实现；(3)数字硬件实现，(4)用2-D递归数字结构实现。

Abstraction :This paper analyzes the principle of Butterworth digital filter,discuss bilinear transformation method of filter design;record a piece of voice by Microsoft voice recorders, carry on its a time-domain analysis, spectral analysis;then design a specified Butterworth band-stop filter based on the theory of bilinear transform,analyze the filter by the tool named Fvtool;and filter the voice signal acquired by voice recorder.finally compare its characteristics of frequency domain and time domain,study the applications of Butterworth filter in digital signal processing ,in particular in signal denoising.

本文分析了巴特沃思数字滤波器的原理，探讨了双线性变换法设计滤波器的方法；用微软录音机采集一段语音，对其进行了时域分析，频谱分析；然后使用双线性变换法设计了一个的巴特沃思带阻滤波器，并且使用fvtool对设计的滤波器进行分析；然后利用该滤波器对采集的语音信号进行滤波。最后对比滤波前后的语音信号的时域和频域特性，研究了巴特沃思滤波器在信号处理尤其是信号滤波去噪方面的特性和应用。

Cklund transfo- rmation、Inverse scattering method、Darboux transformation、Hirota bilinear method、similarity reduction eta.

cklund变换法、反演散射方法、达布变换法、Hirota双线性方法、相似约化法等。

In binary arithmetic, a complementation process where all the1's in a binary number are changed to0's and vice versa.

二进制运算中的一种求反过程，在这种过程中，二进制数中的所有1都变换成0，所有的0都变换成1。

Subline matching method based on binary system small wave transform is proposed, which expliots the character that the model maximum point of spline binary small wave transform coefficient at different scales can provide position information of signal's fast changing point. The matching scheme from thick to thin for point matching is adapted. Then, the point to point matching is calculated with the sequence consistent principle in each subline.

设计基于二进小波变换的子线段匹配方法，通过求解样条二进小波变换系数在不同尺度下的模极大点确定不同尺度下信号急速变化点位置，采用由粗到细的匹配策略匹配端点，再对端点之间的每一个子线段采用顺序一致的原则，进行点对点匹配。

In the image feature extraction stage, both global image features and local image features are introduced in this paper including gray-scale pixel values, Gabor Wavelet Filter, Local Binary Pattern, Scale Invariant Feature Transform and etc. In our experiments we focused more on Scale Invariant Feature Transform method and analyzed the detailed performances of these different methods for representing gender information.

在性别特征提取阶段，文中详细讨论了人脸图像全局特征和局部特征的提取方法，例如基于图像灰度的全局特征提取方法，基于小波滤波器变换的特征提取方法和基于局部二值模式的特征提取方法等，并提出了一种基于尺度不变性的特征变换提取方法。

The measure transformation law of the binomial tree model and its deduction are obtained, analogous to continuous model.

类似于连续情形的测度变换，获得了二叉树模型的一个测度变换定理和推论。

After wavelet transform and quantification,a prediction module was introduced to estimate the entropy of EBCOT code block within available bit plane,then the summation estimate entropy of each image was used to allocate the rate for each image to eliminate influence of the reconstructed image quality using equal allocation.

利用干涉多光谱图像成像推扫平移特性，在小波变换中使用运动补偿来减少帧间相关性，并对图像组中各个图像小波变换和量化后EBCOT编码码块的有效比特平面进行独立的熵估计。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。