查询词典 convolution theorem

The high frequency signals and noise signals are first decomposed into three different directions by making use of the 2-dimensional Daubechies wavelet transform to process matrix data with row convolution and line convolution.

利用二维db小波变换对矩阵数据分别进行行卷积和列卷积，把检测数据的高频信号和噪声信号分解在3个不同的方向上，且信号的能量集中在很少的小波系数上。

By the alternating direction implicit and current density recursive convolution technologies for the first time, a new current density recursive convolution alternating direction implicit finite-difference time-domain (CDRC-ADI-FDTD) formulation for collision unmagnetized plasma is presented.

首次把交替方向隐式技术与等离子体的电流密度递归卷积技术结合，给出了碰撞非磁化等离子体的CDRC-ADI-FDTD方法。

A method of processing a series of input audio signals representing a series of virtual audio sound sources placed at predetermined positions around a listener to produce a reduced set of audio output signals for playback over speaker devices placed around a listener, the method comprising the steps of: for each of the input audio signals and for each of the audio output signals: convolving the input audio signals with an initial head portion of a corresponding impulse response mapping substantially the initial sound and early reflections for an impulse response of a corresponding virtual audio source to a corresponding speaker device so as to form a series of initial responses; for each of the input audio signals and for each of the audio output signals: forming a combined mix from the audio input signals; and forming a combined convolution tail from the tails of the corresponding impulse responses; convolving the combined mix with the combined convolution tail to form a combined tail response;for each of the audio output signals: combining a corresponding series of initial responses and a corresponding combined tail response to form the audio output signal.

提供了一种处理一系列输入音频信号的方法，所述输入音频信号代表放置在收听者周围预定位置的一系列虚拟的音频声源，该方法可以产生一组精简的用于在收听者周围的扬声器装置上进行播放的音频输出信号，该方法包括以下步骤：对每个输入音频信号和每个输出音频信号进行以下步骤：用相应的脉冲响应最初的头部对输入音频信号进行卷积以形成一系列初始响应，其中的脉冲响应充分映射了相应的虚拟声源到相应的扬声器装置的脉冲响应的初始声音和早期反射；对每个输入音频信号和每个输出音频信号进行以下步骤：形成音频输入信号的混音；并根据对应脉冲响应的多个尾部形成复合的卷积尾；用复合的卷积尾对音频信号的混音进行卷积以形成复合尾部响应；对每个音频输入信号进行以下步骤：把相应系列的初始响应与相应的复合尾部响应进行复合以形成音频输出信号。

There are two difficult points in convolution integral: how to determine the limit of the integral, arid the integrands on the convolution integral.

确定卷积积分的积分限和在相应区间上的被积函数是计算卷积积分的两个难点。

DFT using the convolution nature for two complex sequence of linear convolution.

利用DFT的卷积性质求两个复序列的线性卷积。

In the first part of the second chapter,we obtain a equivalent condition of the convolution closure of the extended long-tailed distributions,generalize and improve the corresponding results of Pakes(2004),and then receive a kind of equivalent conditions of convolution-equivalence distributions.In the last part of the second chapter,we prove these results.

本文第二章的前一部分得到了有关广义长尾分布的卷积封闭性的等价条件，推广和改进了Pakes(2004)的一个相应结果，进而得到一类卷积等价分布的等价条件；第二章的后一部分证明了这些结果。

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顾了高斯之前的数论研究状况，在系统分析高斯的科学与数学成就的基础上，探讨了《算术研究》出现的数学背景和高斯的同余理论；(2)通过对原始文献的系统解读，深入分析了费马小定理发现发展的历程以及在素性检验中的重要作用，指出《算术研究》前三节是高斯在总结并发展了前人对该定理研究的基础上形成的，并揭示了费马小定理在初等数论定理证明中的核心地位；(3)以二次互反律的两个主要来源为线索，详细考察了费马，欧拉，拉格朗目，勒让德，直到高斯的相关工作，揭示了该定律对十九世纪数论发展的巨大推动作用。

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。