Alias-Component Matrices of Multirate Systems

We consider a multirate system, which is a generalization of linear time-invariant systems. Such a system is invariant to a certain shift in the input sequence. In particular, assume that p and q are coprime. A multirate system with the property that a delay of mq samples in its input sequence results in a delay of mp samples in its output sequence is called an (mp, mq)-periodic system. This multirate system can be obtained by cascading an upsampler, followed by a linear periodically time-varying (LPTV) kernel system, then followed by a downsampler. Here, we study the alias-component matrices of multirate systems. We show that they can be obtained from the alias-component matrices of their LPTV kernels by some row and column additions. An example shows the use of the method to design rate changers for a specified frequency band swap.     

基于非均匀滤波器组的动态信道化滤波

针对中频带宽内存在多个子带信号,其个数、位置和带宽具有时变性的情况,该文提出一种基于非均匀滤波器组的动态信道化滤波的方法：由事先给定的子带信号间的最小保护间隔确定均匀滤波器组的子信道数目并设计相应的余弦调制滤波器组;由子带信号的位置分布求得非均匀处理矩阵,并由此直接合并余弦调制滤波器组的对应的相邻子信道以构成非均匀滤波器组;当信号动态变化时,只要根据新状态下的子带信号位置分布更新非均匀处理矩阵,就能完成新信号的信道化接收;利用不同子带信号的抽取因子之间的大小关系提前部分抽取因子以降低实现过程的运算量。仿真实例验证了新方法的有效性。     

Design of Nonuniform Transmultiplexers with Block Samplers and Single-Input Single-Output Linear Time-Invariant Filters Based on Perfect Reconstruction Condition

This paper proposes a design of a nonuniform transmultiplexer with block samplers and single-input single-output linear time-invariant filters. First, the perfect reconstruction condition of the nonuniform transmultiplexer is derived. Then, the design problem is formulated as an optimization problem. In particular, the perfect reconstruction error is minimized in the \(L_{1}\) norm sense subject to the frequency selectivities of the filters. Computer numerical simulation results show that the designed nonuniform transmultiplexer with block samplers is robust to the channel noise and achieves a small reconstruction error.     

对合Cauchy-Hadamard型MDS矩阵的构造

MDS矩阵和对合MDS矩阵在分组密码中有广泛应用。该文将考察同时是Hadamard矩阵和Cauchy矩阵的那些MDS矩阵,给出了这类矩阵的结构、构造方法和个数,从而得到了MDS矩阵一种新的构造方法。该文还证明了Cauchy-Hadamard型MDS矩阵都等效于对合的Cauchy-Hadamard型MDS矩阵,并给出了由Cauchy-Hadamard型MDS矩阵构造对合的Cauchy-Hadamard型MDS矩阵的方法。     

具有最小异或数的最大距离可分矩阵的构造

随着物联网等普适计算的发展,传感器、射频识别(RFID)标签等被广泛使用,这些微型设备的计算能力有限,传统的密码算法难以实现,需要硬件效率高的轻量级分组密码来支撑。最大距离可分(MDS)矩阵扩散性能最好,通常被用于构造分组密码扩散层,异或操作次数(XORs)是用来衡量扩散层硬件应用效率的一个指标。该文利用一种能更准确评估硬件效率的XORs计算方法,结合一种特殊结构的矩阵—Toeplitz矩阵,构造XORs较少效率较高的MDS矩阵。利用Toeplitz矩阵的结构特点,改进矩阵元素的约束条件,降低矩阵搜索的计算复杂度,在有限域${\mathbb{F}_{{2^8}}}$上得到了已知XORs最少的4×4MDS矩阵和6×6MDS矩阵,同时还得到XORs等于已知最优结果的5×5MDS矩阵。该文构造的具有最小XORs的MDS Toeplitz矩阵,对轻量级密码算法的设计具有现实意义。     

超宽带开关矩阵的研制

介绍了一种采用p-i-n开关设计的单路选通开关矩阵。通过合理设计p-i-n二极管的直流反偏电压,解决了p-i-n开关矩阵承受功率的设计问题;采用宽带锥形电感和空心电感相结合的电路形式,设计了一种宽带的偏置电路;优化了开关矩阵电路的设计,简化了电路结构形式,提高了开关矩阵的微波性能和可生产性。设计实现了一种超宽带单路选通开关矩阵,工作频率为1～18 GHz,插入损耗(IL)<5 dB,端口隔离(Isolation)>35 dB。验证结果表明,理论仿真结果与实验测试结果基本一致,证明了设计方法的可行性。     

集成光开关阵列的研究进展

文中简要介绍了集成光开关阵列的研究进展,重点分析了不同材料和不同结构的开关 阵列的特点:绝缘体上的硅(SOI) 和III - V 族化合物半导体光开关阵列是阵列开关研究的重点,完全无阻塞简化树型和拜尼兹重排无阻塞型阵列开关有良好的综合性能,半导体光放大器(SOA) 光开关阵列已成为未来阵列开关发展的重要方向之一。     

一种基于形状矩阵的傅立叶描述子

提出了一种基于形状矩阵的傅里叶描述子,该算法首先对植物叶片图像二值化,随后将图像的直角坐标转换为极坐标,并将极点移至图像质心,再利用极坐标光栅系统对图像重新采样形成形状矩阵,之后对矩阵进行离散傅里叶变换,利用低频系数描述图像的形状信息。实验结果显示该方法的检索性能明显优于Hu不变矩、等面积同心圆等其他5种算法,在对图像的抗噪性实验中也证明了该算法的高效性。     

相关跳频转移函数的双随机矩阵模型及其应用

该文分别从状态空间的分解和平稳分布等角度对双随机矩阵以及双随机马氏(Markov)链的性质进行了研究,并将这些性质应用到相关跳频转移函数的分析和建模。文中证明了转移函数的双随机矩阵数学模型就状态转移过程的均匀性来说是完备的。基于对该模型的分析,提出了一种转移函数构造方法周期分组法,通过将频率转移过程构造成一个周期性双随机马氏链,可以获得纠错性能和频率间隔性能俱佳的转移函数。     

CS-DOA 估计中观测矩阵性能分析

利用压缩感知(CS)理论解决阵列信号波达方向角(DOA)估计问题,具有对快拍数据量要求低、可处理相关源等优点。CS鄄DOA 估计中的一个关键问题是构建合适的观测矩阵。文中对比分析了均匀线阵与随机稀布阵两种阵列流形的稀疏重构性能,分析结果表明在实际应用中基于随机稀布阵构建的观测矩阵性能更优。仿真实验从三个方面比较了两种观测矩阵的DOA 估计性能,验证了随机稀布阵性能的优越性,在不增加阵元数的前提下,能有效提高阵列的空间角分辨率。     

用波形迭代法分析非均匀多导体传输线的时域响应

本文从频域电报方程出发推出了一个描述传输线ABCD矩阵的微分方程,将传输线时域响应分析从微分方程的边值问题转化为数学上更易求解的初值问题。然后利用波形迭代法数值求解非均匀传输线的ABCD矩阵,证明了一个关于迭代收敛性的定理,并据此采取了旨在加快收敛速度的将传输线分割成许多相互级联的子网络的步骤。传输线的ABCD矩阵求得后,便可借用付里叶变换和卷积技术对具有线性、非线性负载的传输线时域响应进行分析。给出的应用实例表明,诙分析方法是有效而可靠的。     

遍历矩阵及其单向限门函数在密码学中的应用

单向限门函数在公钥密码学中有着重要的应用。文章基于遍历矩阵良好的加密特性构造了一个单向限门函数,实现其在对称密钥加密、混合密钥加密、STS密钥协议以及Shamir三次传递协议中的应用,并从理论上证明,遍历矩阵在各种攻击条件下具有较高的防破解能力,因此具有很高的安全性。     

Optimal design of nonuniform multirate filter banks

The design of general nonuniform filter banks is studied. Contrary to uniform filter banks, in nonuniform filter banks, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we can design acceptable filter banks. Here, the initial finite impulse response (FIR) analysis filters are designed according to the characteristics of the input. By the design procedure, the FIR synthesis filters are found so that theH-norm of an error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed, and the analysis filters are found similarly. By iteration, theH-norm of the error system decreases until it converges to its final value. At each iteration, the coefficients of the analysis or synthesis filters are obtained by finding the least squares solution of a system of linear equations. If necessary, the frequency characteristics of the filters can be altered by adding penalty terms to the objective function.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

基于循环转置单位矩阵条件填充的LDPC码构造方法

通过分析并充分利用循环转置单位矩阵在环中的特性,该文提出了一种基于转置矩阵条件填充的LDPC码构造方法,给出了按此方法构造的校验矩阵最小环长的上、下理论限,并在此基础上提出了一种具体的条件填充构造法,仿真结果表明,该方法能够明显减少校验矩阵的最小环数目,较大程度上提升了码子性能。     

一种基于循环移位矩阵的LDPC码构造方法

具有准循环结构的低密度奇偶校验码(QC-LDPC Codes)是目前被广泛采用的一类LDPC码。本文提出了一种结合PEG算法构造基于循环移位矩阵的QC-LDPC码的方法。该方法首先将QC-LDPC码传统的基于比特的二分图简化为基于Block的二分图,然后在该图中采用PEG算法遵循的环路最大原则确定每一个循环移位矩阵的位置,最后根据QC-LDPC码的环路特性为每一个循环移位矩阵挑选循环移位偏移量。利用该算法,本文构造了长度从1008bit到8064bit,码率从1/2到7/8各种参数的LDPC码。仿真结果表明,本文构造的LDPC码性能优于目前采用有限几何、两个信息符号的RS码、组合数学等常用的代数方法构造的QC-LDPC码。     

稀疏随机矩阵的观测次数下界

压缩感知理论中的稀疏重构问题,要将一个高维信号从它的低维投影中恢复出来,通常选用稠密随机矩阵作为观测矩阵来解决这一问题。而某些稀疏随机矩阵作为观测矩阵也可以达到这一目的。稀疏随机矩阵的特点是,在编码和重构过程中都具有较低的计算复杂度,更新方便,且对存储容量的要求较低。该文基于压缩感知理论,分别对列重固定、行重固定以及一般的稀疏随机矩阵进行了研究,当这些稀疏随机矩阵满足有限等距性质时,推导了观测次数应满足的下界条件,并对三种矩阵的性能进行了分析。以二值稀疏随机矩阵为特例,进行了仿真实验。实验结果显示,结论给出的观测次数下界是比较紧的,并验证了列重固定、行重固定的稀疏随机矩阵作为观测矩阵的可行性和实用性。      

A Class of Multimode Transmultiplexers Based on the Farrow Structure

This paper introduces multimode transmultiplexers (TMUXs) in which the Farrow structure realizes the polyphase components of general lowpass interpolation/decimation filters. As various lowpass filters are obtained by one set of common Farrow subfilters, only one offline filter design enables us to cover different integer sampling rate conversion (SRC) ratios. A model of general rational SRC is also constructed where the same fixed subfilters perform rational SRC. These two SRC schemes are then used to construct multimode TMUXs. Efficient implementation structures are introduced and different filter design techniques such as minimax and least-squares (LS) are discussed. By means of simulation results, it is shown that the performance of the transmultiplexer (TMUX) depends on the ripples of the filters. With the error vector magnitude (EVM) as the performance metric, the LS method has a superiority over the minimax approach.     

2-Norm Based Recursive Design of Transmultiplexers with Designable Filter Length

In this paper, motivated by the facts that shorter length filters offer considerable improvements in computation and hardware implementation and that designable filter length brings more design flexibility, we propose a novel transmultiplexer design method that can not only achieve close-to-perfect reconstruction but also obtain designable filter length. The proposed method is based on a composite distortion measure: the 2-norm of the error transfer matrix of the transmultiplexer. Central to the development is providing an efficient means to recursively design the filters in the transmultiplexer and evaluating the composite distortion measure, which greatly improves the computation efficiency. The simulation results show the effectiveness of the proposed algorithms.     

Energy‐Dissipative Matrices Enable Synergistic Toughening in Fiber Reinforced Soft Composites

Tough hydrogels have shown strong potential as structural biomaterials. These hydrogels alone, however, possess limited mechanical properties (such as low modulus) when compared to some load‐bearing tissues, e.g., ligaments and tendons. Developing both strong and tough soft materials is still a challenge. To overcome this obstacle, a new material design strategy has been recently introduced by combining tough hydrogels with woven fiber fabric to create fiber reinforced soft composites (FRSCs). The new FRSCs exhibit extremely high toughness and tensile properties, far superior to those of the neat components, indicating a synergistic effect. Here, focus is on understanding the role of energy dissipation of the soft matrix in the synergistic toughening of FRSCs. By selecting a range of soft matrix materials, from tough hydrogels to weak hydrogels and even a commercially available elastomer, the toughness of the matrix is determined to play a critical role in achieving extremely tough FRSCs. This work provides a good guide toward the universal design of soft composites with extraordinary fracture resistance capacity.