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Among many implement schemes of decoding, the one using chips is the fastest one. Specific decoding chips like FPGA or ASIC have parallel processing structures, which make them be much fit for being high performance data processing processors like Digital Filter, Fast Fourier Transform, Discrete Cosine Transform, etc, and also be the key part of high performance data processing systems. The implementation is synthesizable Verilog code at the RTL level. It is suitable for real time video applications.

在MP3 解码电路中，模块IMDCT 由三个子模块组成：IDCT子模块、加窗函数子模块、输出数据的叠加子模块。N/2 点的输入Xk 经IDCT 变换得到N 点的输出xi 的公式如下：将输出根据不同的块类型(有四种块类型，分别为普通、开始、结束、短型)采用不同的窗函数加窗，得到一个36 个点的输出(对于块类型为短型的块，单个小块的输出是12 个点，每三个小块组合成一个36 个点的输出)。

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。

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。