Convolution algorithms,based on the crt (Chinese Remainder Theorem)

It is well-known that most contemporary algorithms for calculating discrete convolutions are based on the Chinese remainder theorem (CRT). In this paper, the problem of calculating convolutions or equivalently, polynomial products, is addressed from the opposite point of view. Instead of showing how a given polynomial product (most often, a circular convolution) can be calculated by means of the CRT, we investigate which polynomial product algorithms make the most efficient use of the CRT. One set of polynomial product algorithms is subsequently discussed in detail. Amongst others, it is shown that the circular convolution is the most efficient representative in this set.     

A Convolution and Correlation Theorem for the Linear Canonical Transform and Its Application

As a generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) plays an important role in many fields of optics and signal processing. Many properties for this transform are already known, but the correlation theorem, similar to the version of the Fourier transform (FT), is still to be determined. In this paper, firstly, we introduce a new convolution structure for the LCT, which is expressed by a one dimensional integral and easy to implement in filter design. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, based on the new convolution structure, the correlation theorem is derived, which is also a one dimensional integral expression. Last, as an application, utilizing the new convolution theorem, we investigate the sampling theorem for the band limited signal in the LCT domain. In particular, the formulas of uniform sampling and low pass reconstruction are obtained.     

Face completion with Hybrid Dilated Convolution

Image completion is a challenging task which aims to fill the missing or masked regions in images with plausibly synthesized contents. In this paper, we focus on face image inpainting tasks, aiming at reconstructing missing or damaged regions of an incomplete face image given the context information. We specially design the U-Net architecture to tackle the problem. The proposed U-Net based method combines Hybrid Dilated Convolution (HDC) and spectral normalization to fill in missing regions of any shape with sharp structures and fine-detailed textures. We perform both qualitative and quantitative evaluation on two challenging face datasets. Experimental results demonstrate that our method outperforms previous learning-based inpainting methods. The proposed method can generate realistic and semantically plausible images.     

卷积性质综合训练的探讨

在"信号与系统"课程教学中,为加强学生对知识的掌握,本文利用卷积性质等相关知识设计了回音信号产生和消除的综合训练题目。文中详细介绍了回音产生和消除的基本原理,对学生设计中出现的问题予以讨论启发。这种综合训练培养了学生独立科学思考、创新发展和解决问题的能力。     

Convolution revisited

Few mathematical operations are more important to the engineer than convolution and transform analysis. In this article, the operation of convolution is explored?starting with discrete rather than continuous convolution because of the relative ease of comprehension involved. With this foundation, the study is extended to continuous convolution. A proof of the convolution theorem will show that convolution and transform analysis are closely related. Of much more interest, however, is an intuitive explanation of why convolution and transform analysis techniques lead to exactly the same solution of a given problem. Perhaps the two most important applications of convolution deal with the analysis of linear systems and the sums of independent random variables?the latter problem being used to introduce discrete convolution.     

Assessing Reliability by Multidimensional Convolution with Quantization

Consider a system with several input parameters; each input is a stochastic variable. The joint probability of all system outputs simultaneously meeting their specifications is found by a hitherto unpublished method called ``Multi-dimensional Convolution with Quantization.' To use the method, two assumptions must be satisfied; the assumptions are milder than the two popular assumptions of linearity and statistical independence. There is one example.     

FDA-MIMO雷达噪声卷积式干扰抑制方法

基于数字射频存储器（digital radio frequency memory,DRFM）产生的噪声卷积灵巧干扰兼具压制式和欺骗式干扰的效果,严重降低了雷达系统的探测性能。为解决此问题,本文提出了一种采用频率分集阵（frequency diversity array,FDA）-多输入多输出（multiple-input-multiple-output,MIMO）雷达的噪声卷积灵巧干扰对抗方法。经由雷达发射信号和噪声信号卷积调制所得的干扰信号在距离-多普勒维与目标回波呈现不同的分布特性。据此,首先利用干扰信号在多普勒域的白噪声特性获取多普勒清晰区的干扰样本,然后在此基础上逐距离门挑选样本以获得干扰协方差矩阵,最后通过距离-角度二维匹配滤波器抑制距离不匹配的主瓣干扰信号。仿真试验验证了本文所提抗干扰方法的有效性。     

利用网格卷积特征的三维形变目标分类

三维目标的形状变化给目标识别带来很大挑战,同时三维网格模型的不规则数据结构难以直接应用卷积运算提取三维目标特征.对此,本文提出了一种高效的三维形变目标的网格卷积特征表示方法,准确提取形状信息并进行分类.首先通过网格卷积运算获得形变目标中典型局部曲面形状分布,其次通过马尔科夫链对曲面形状的空间共现关系建模,从而形成三维模型的全局特征描述,最后采用支持向量机实现形变目标分类.该方法将连续多项式函数作为卷积模板,实现针对不规则数据结构的网格卷积运算,并且给出了卷积模板参数的无监督学习方法.在标准非刚性三维模型数据集SHREC10与SHREC15上的实验结果表明本文方法能有效提取三维网格模型的形状信息,分类准确率分别达到了92.88%与96.54%.     

采用深度可分离卷积和改进特征融合的MSSD

单步多框检测器(Single Shot Multibox Detector,SSD)是一种优秀的目标检测模型,但是其对额外层的处理方式还需要进一步提升.因此,利用深度可分离卷积的思想设计新的深度可分离卷积模块改进模型中的额外层,采用紧邻特征图融合方法加强特征复用,综合设计了改进的目标检测模型(Modified SSD,...     

基于Mathematica的卷积计算

介绍了用Mathematica计算连续信号卷积和离散信号卷积和的方法。所提出的方法可得到连续信号卷积的精确解析解,而非用Matlab得到的近似解。对于离散信号,无论是有限长序列还是无限长序列的卷积和均可求解。与传统计算方法相比,该方法避开了繁琐的做图或积分求和过程,使计算更简便、快速。     

用卷积运算实现反卷积

本文首先简介了用卷积运算实现反卷积的原理、方法和实例;其次,提出了该方法的病态问题,并给出了解决的办法;最后,给出了这种方法的估计误差及实例.     

Convolution by membrane waves

Convolution in the frequency range of hundreds of kilohertz has been produced by using the nonlinear relationship between longitudinal strain and transversal displacement associated with the membrane wave. The transversal piezoelectric effect of PVF2 film has been used to detect convolution.     

因果移序定理及其应用

本文给出了因果移序定理的时域、z域和状态方程表达式，证明了因果移序定理在离散系统的时域、z域和状态方程分析中的重要地位和作用。这些表达式不但使得系统分析简捷清晰，而且物理概念清楚。各章之间的内在联系也可交待清楚，这十分有利于学生的理解和消化。我们历年的“信号与系统”的教学实践有力地证明了这一点。     

因果微分定理及其应用

本文给出了因果微分定理的时域、频域、s域和状态方程表达式,重点讨论了因果微分定理在LTI系统的时域分析中的应用,证明了因果微分定理在系统的时域、频域、s域和状态方程分析中的重要地位和作用.它们不但使得系统分析简捷清晰,而且物理概念清楚.各章之间的内在联系交待清楚,十分有利于学生的理解和消化.通过历年的"信号与系统"的教学实践证明了这一点.     

戴维南定理教学中强化定理思维培养的探索

在戴维南定理讲授过程中引入了叠加定理、替代定理之外的第三个定理——“等效电阻定理”,该定理既能在问题引入环节启发思考,又可以补齐戴维南定理证明过程中的全逻辑链条,还有助于从逻辑推演的方式得出新定理的适用条件。基于逻辑推演的严密性,抽象出一种同时适用于白箱电路和黑箱电路的等效电阻参数通用求取方法——内部电源法,有助于拓展开路电压/短路电流法的内涵,其与“外加电源法”在名称上的对照也有助于掌握等效电阻求取的操作要领。     

利用PD雷达脉冲压缩实例讲解分段卷积

“数字信号处理”课程中的分段卷积是来源于工程实践的解决方案,但学生经常对这个知识点的重要性认识不足。本文以PD雷达中对回波信号的脉冲压缩处理为例,介绍什么情况下会出现“ ”这个分段卷积的前提条件,以及分段卷积在实时信号处理中的工程价值。     

用FPGA实现DVB标准中的卷积交织

卷积编码是数字传送前向纠错编码中用来解决突发性干扰的有效手段。本文介绍了用FPGA(现场可编程门阵列)器件实现卷积交织编码器,分析了其基本原理和实现过程。     

Convolution theorems for linear transforms

This correspondence explores the existence of convolution theorem for linear transformations under a variety of different assumptions. There are eight convolution theorems, all Fourier-related with only N operations in the transform domain and no ordering constraints on the convolution components in the result. They include circular convolutions and correlations     

LFM信号的卷积调制干扰仿真

线性调频脉冲信号在雷达中应用广泛,其优点是具有脉内相干性。传统的噪声干扰进入雷达后无法获得处理增益,因而在功率有限的情况下往往干扰效果不佳。相对于噪声干扰,卷积调制干扰的优点是可获得雷达较大的处理增益。对基于LFM信号的卷积调制干扰进行了理论分析,并对该信号进入雷达后的干扰效果进行了仿真。