卷积定理

一维Z变换中的卷积定理研究

On Convolution Theorem of 1D Z Transform

本文引进并研究α级凸象函数类的一个子类K（λ，α），证明了包含关系和卷积定理；

In this paper , We introduce and study a subclass K (λ, α) of convex functions of order α . We prove an inclusion relation and a convolution theorem .

该定理与卷积定理配合，在一般系统中，只要已知输入函数x（t）、系统函数h（t）及输出函数y（t）中的任意两个，便可求得第三个函数。

In general system , if two of inputting function , system function and outputting function are known , the other may be known certainly according to the de convolution theorem and the convolution theorem .

在此基础上，利用Fourier逆变换和卷积定理，求得了半正弦脉冲激励作用下桩顶速度时域响应的半解析解。

By means of inverse Fourier transform technique and convolution theorem , the semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pile head is obtained in the time domain .

本文应用DFT的重迭保留法和循环卷积定理、LMS算法原理，导出了频域自适应滤波的LMS算法的公式。

On the basis of overlap save method and circular convolution theorem in the DFT , by LMS algorithm , formulas of LMS algorithm of the frequency-domain adaptive FIR digital filter are yielded .

该文给出了二维时域卷积定理的完整描述，包括二维单边、双边时域序列及二维单边、双边Z变换的不同组合情形下，时域卷积定理的描述及定理的证明。

This paper gives a complete description of 2-D time-domain convolution the-orem , including the rigid proof of different combinations of 2 . D two-sided and / or one-sided time sequences and 2-D one-sided and / or two-sided Z-transform .

进一步结合平面应变模型，通过Laplace变换和卷积定理等数学方法，求得任意激振力作用下的桩体振动频域响应解析解和时域响应半解析解。

Further , in combination with the plane strain model , the analytical solutions of longitudinal vibration response of piles in frequency domain and the corresponding semi-analytical solutions in time domain were obtained using Laplace transform and convolution theorem .

利用Γ函数和它的对数微商的一些性质以及Laplace变换的卷积定理，Γ函数的一个凸性结果被获得.作为应用，著名的Wallis不等式被改进。

By using some properties of Γ function and its logarithmic derivative , and the convolution theorem for Laplace transforms , a convexity result of Γ function is obtained . As an application , the well-known Wallis ' inequality is refined .

双边截断分布族中的卷积定理与渐近有效性

Convolution Theorem and Asymptotic Efficiency in Two Side Truncated Distribution Families

基于卷积定理和希尔伯特变换的模拟调制分析

Analysis of Analog Modulation Based On Convolution Theorem and Hilbert Transform

研究了Sα（λ，β）中函数的某种积分运算及卷积定理。

Study some integral operation and hadamard theorems of functions in S_ α (λ,β) .

值得一提的是，文中利用卷积定理处理信号模糊函数的形式，对其它任何信号都具有普遍的适用性。

Convolution theory used to process signal ambiguity function in the paper is also applicable to other signals .

在时移问题上，通过相关函数、卷积定理和功率谱定理来理解并矢时间这一新概念的意义。

On the time shift problems , the significance of the new concept of dyadic time has been interpreted .

研究了线性定常系统的时域分析，给出了几个求解线性定常系统的卷积定理。

Studies time domain analysis of linear system with constant parameters , and presents some convolution theorems for solving linear system with constant parameters .

然后利用卷积定理和傅立叶逆变换求得瞬态半个正弦波作用下桩顶响应的振动半解析解；

Further , with the help of the convolution theorem and inverse FOURIER transform , a semi-analytical solution of the velocity response under semi-sine impulse exciting is obtained .

利用拉氏变换和卷积定理，分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。

Analytical solutions are obtained using Laplace transform and convolution theorem for the transient wave motion in saturated porous media under arbitrary stress boundary condition and displacement boundary condition , respectively .

本方法的关键是通过卷积定理把电子浓度涨落的时间自相关函数与能通过带电粒子的无干扰轨道直接计算出来的函数联系起来。

The key lies in applying the convolution theorem to relate the time autocorrelation of electron density fluctuations with the function which can be directly calculated from the unperturbed orbits of charged particles .

本文继续研究〔1〕中引进的线性同胚于星象函数的一族解析函数A，给出了A族的卷积定理以及系数和的一个不等式。

This paper continues to study a family analytic functions A of linear homeomorphic and starlike functions in [ 1 ] introduced . We give the convolution theorem of family A ( A , or ) and an inequality of coefficient sum .

针对一维及二维离散Hartley变换分别建立了其修正循环卷积特性定理。籍此可得计算循环卷积的快速Hartley变换法。

This paper derives the modified cyclic convolution properties of Discrete Hartley Transforms ( DHT ), upon which the fast Hartley transform method for computing cyclic convolutions is obtained .

首先，对关于n-折对称点的星像与凸像函数，给出了包含关系、积分表示、卷积条件、增长定理、覆盖定理与偏差定理。

Firstly , for starlike and convex functions with respect to n-fold symmetric points , we obtain inclusion relationships , integral representations , convolution conditions , growth theorems , covering theorems and distortion theorems .

其次，推导了一般线性正则变换的卷积表达形式，根据傅里叶变换的卷积定理，由快速傅里叶变换实现卷积计算。

So that the discrete Gyrator transform can be calculated by the Fast Fourier transform . The convolution expression of the general linear canonical transform has been derived . So it can be calculated by the Fourier transform according to the convolution theorem of Fourier transform .