非线性动力学常微分方程组高精度数值积分方法

建立了一种求解非线性动力学常微分方程组初值问题的新方法．若非线性函数一阶导数存在，则给出解的积分方程表达式，计算得到按规定误差要求的高精度数值解．引入一般自治或非自治非线性系统的首次近似Jacobi矩阵，不作任何假设重构等价的非线性常微分方程组，简捷而有广泛的适应性，不改变方程的本质，但其主项构成线性化方程组，其它项则代表非线性函数高阶余项而不涉及Taylor级数展开计算，给出该方程组初值问题的Duhamel卷积分解析表达式，在时间步长内进行数值积分选代求解，在指定误差内快速收敛，逐步递推获得非线性常微分方程的瞬态响应和全时域高精度数值解．积分解连续满足微分方程组而不是在离散的步长端点上满足代数方程组，打破了传统用增量法在离散点上建立的代数方程组迭代求解，从而使传统Euler型逐步积分法的各种差分格式算法改变成真正的积分格式算法．数值计算中给出指数矩阵递增展开式，变矩阵乘法为乘积系数的加法，避免了大量矩阵自乘而大大提高计算效率．算法验证为无条件稳定，则保证对线性常微分方程而言，计算中舍入误差的传播不会扩散，不出现计算机字长有限而引起舍入误差导致计算不确定性问题．基于以上理论和数值方法，计算了线性非线性算例并进行了分析，验证了本方法简捷而有广泛的适应性，可以有足够的精确性．     

无人机数据链中卷积码研究与FPGA实现

信道编码是数字通信系统中的重要组成部分,它是保证信号可靠传输的一种重要方式,卷积码以其优越的性能被广泛应用在数字通信系统中。结合无人机信道的特性,研究分析了卷积码的性能特征,选定了适合无人机数据链特性的（2,1,2）卷积码,采用硬件描述语言实现了卷积码编译码器的硬件设计。实验结果表明,在纠错能力范围内,该设计方案能够正确纠错并译码,并且具有较高的译码速率,提高了无人机数据链的通信质量和抗干扰性能。     

一种2-D循环卷积数据的构造方法

考虑到循环卷积在二维（2-D）信号处理中的重要作用,研究了2-D循环卷积数据的构造问题。基于信号处理中2-D卷积理论,首先着重分析了循环卷积数据和线性卷积数据、以及非完全线性卷积数据的特殊关系。基于该关系,给出了一种利用2-D非完全线性卷积数据构造2-D循环卷积数据的有效方法,该方法通过将非完全线性卷积分成相应子块,继而进行合并,实现了循环卷积数据的构造。实验仿真结果显示了提出方法的有效性。     

Approximation in weighted p-mean by RBF networks of Delsarte translates

We give conditions on the kernel function (or activation function) for the family of radial basis function (RBF) neural networks obtained upon replacing the usual translation by the Delsarte one, with not necessarily the same smoothing factor in all kernel nodes, to have the universal approximation property in suitable weighted L^p$L^p$-spaces (1?p<∞)$(1?p<\infty )$. A complete characterization of such kernels for p=1$p=1$ and p=2$p=2$ is provided.     

An ultra-fast smoothing algorithm for time–frequency transforms based on Gabor functions

Gabor functions, Gaussian wave packets, are optimally localized in time and frequency, and thus in principle ideal as (frame) basis functions for a wavelet, windowed Fourier or wavelet-packet transform for the detection of events in noisy signals or for data compression. A major obstacle for their use is that a tailored efficient operator acting on the transform coefficients for altering the width of the wave packets does not exist. However, by virtue of a curious property of the Gabor functions it is possible to change the width of the wave packets using just one-dimensional convolutions with very short kernels. The cost of a wavelet-type transform based on the scheme presented below is similar to that of a low order wavelet transform for a compact kernel and significantly less than the algorithme à trous. The scheme can hence easily be employed for the processing of signals in real time.     

Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.     

On the modulus of continuity for spectral measures in substitution dynamics

The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weak mixing suspension flows over substitution automorphisms, which yield information about the “fractal” structure of these measures. The main results are, first, a Hölder estimate for the spectral measure of almost all suspension flows with a piecewise constant roof function; second, a log-Hölder estimate for self-similar suspension flows; and, third, a Hölder asymptotic expansion of the spectral measure at zero for such flows. Our second result implies log-Hölder estimates for the spectral measures of translation flows along stable foliations of pseudo-Anosov automorphisms. A key technical tool in the proof of the second result is an “arithmetic-Diophantine” proposition, which has other applications. In Appendix A this proposition is used to derive new decay estimates for the Fourier transforms of Bernoulli convolutions.     

一种新型2-D卷积器的FPGA实现

提出了一种基于FPGA实现的新型2-D卷积器结构.该结构占用硬件资源少,外部带宽只需1pixels/clock.与传统的卷积器相比,不仅资源耗用减少95%以上,并且可以依据系统实时性要求调整吞吐率,带来了系统设计的灵活性.在Altera EP4SGX230KF40FPGA上实现结果表明,对于5×5大小的图像卷积,达到90Mpixels/s的吞吐率,满足大多数图像处理系统的实时性要求.     

Best Fourier Approximation and Application in Efficient Blurred Signal Reconstruction

We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results.     

“数字信号处理”中重叠保留法的证明

重叠保留法是计算一个短序列与一个无限长序列线性卷积的有效方法。就我们所知，多数《数字信号处理》教材详细叙述了重叠保留法的步骤，有些教材还从线性卷积与循环卷积的关系出发给出了重叠保留法的原理，笔者认为这种解释不够清楚、也不够严谨。本文给出了一个较为严谨而准确的证明。