Design of digital FIR variable fractional order integrator and differentiator

This paper presents an easy and simple method to design variable fractional order digital FIR integrators and differentiators based on fractional order systems. First, closed-form digital IIR fractional order integrators and differentiators have been obtained from the analog rational functions approximations, in a given frequency band, of the fractional order integrator s ^?m and differentiator s ^m (0?<?m?<?1) through the Tustin generating function. Then, closed-form digital FIR fractional order integrators and differentiators by truncation of the digital IIR ones have been derived. Next, polynomial interpolation has been used to design digital FIR variable fractional order integrators and differentiators that can be implemented by the Farrow structure. The main feature of variable fractional order operator is that its order can be changed without re-designing a new fractional order operator. Some examples have been presented through the paper to illustrate the performance and the effectiveness of the proposed design method. The results obtained have been discussed and have been compared to one of the most recent works in the literature using the same design parameters.     

A joint swarm intelligence algorithm for multi-user detection in MIMO-OFDM system

In the multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) system, traditional multi-user detection (MUD) algorithms that usually used to suppress multiple access interference are difficult to balance system detection performance and the complexity of the algorithm. To solve this problem, this paper proposes a joint swarm intelligence algorithm called Ant Colony and Particle Swarm Optimisation (AC-PSO) by integrating particle swarm optimisation (PSO) and ant colony optimisation (ACO) algorithms. According to simulation results, it has been shown that, with low computational complexity, the MUD for the MIMO-OFDM system based on AC-PSO algorithm gains comparable MUD performance with maximum likelihood algorithm. Thus, the proposed AC-PSO algorithm provides a satisfactory trade-off between computational complexity and detection performance.     

An optimal spectrum‐balancing algorithm for digital subscriber lines based on particle swarm optimization

This paper presents a new algorithm for optimal spectrum balancing in modern digital subscriber line (DSL) systems using particle swarm optimization (PSO). In DSL, crosstalk is one of the major performance bottlenecks, therefore various dynamic spectrum management algorithms have been proposed to reduce excess crosstalks among users by dynamically optimizing transmission power spectra. In fact, the objective function in the spectrum optimization problem is always nonconcave. PSO is a new evolution algorithm based on the movement and intelligence of swarms looking for the most fertile feeding location, which can solve discontinuous, nonconvex and nonlinear problems efficiently. The proposed algorithm optimizes the weighted rate sum. These weights allow the system operator to place differing qualities of service or importance levels on each user, which makes it possible for the system to avoid the selfish‐optimum. We can show that the proposed algorithm converges to the global optimal solutions. Simulation results demonstrate that our algorithm can guarantee fast convergence within a few iterations and solve the nonconvex optimization problems efficiently. Copyright © 2008 John Wiley & Sons, Ltd.     

一种高性能内插滤波器的设计

在全数字接收机系统中,随着高阶调制解调技术的应用,传统内插滤波器的性能已不能满足要求。为此,通过研究一种多项式函数的频率响应,提出了一种高性能内插滤波器的设计方法。该方法在频域逼近的基础上,以线性加权的最小均方误差（MMSE）为优化准则,利用Matlab系统函数进行线性约束条件下的最优化迭代,设计非常灵活。仿真结果表明,该方法设计的内插滤波器性能明显优于常用的内插滤波器,尤其适合于高阶正交幅度调制（QAM）信号。     

Using fractional delay to control the magnitudes and phases of integrators and differentiators

The use of fractional delay to control the magnitudes and phases of integrators and differentiators has been addressed. Integrators and differentiators are the basic building blocks of many systems. Often applications in controls, wave-shaping, oscillators and communications require a constant 90deg phase for differentiators and -90deg phase for integrators. When the design neglects the phase, a phase equaliser is often needed to compensate for the phase error or a phase lock loop should be added. Applications to the first-order, Al-Alaoui integrator and differentiator are presented. A fractional delay is added to the integrator leading to an almost constant phase response of -90deg. Doubling the sampling rate improves the magnitude response. Combining the two actions improves both the magnitude and phase responses. The same approach is applied to the differentiator, with a fractional sample advance leading to an almost constant phase response of 90deg. The advance is, in fact, realised as the ratio of two delays. Filters approximating the fractional delay, the finite impulse response (FIR) Lagrange interpolator filters and the Thiran allpass infinite impulse response (IIR) filters are employed. Additionally, a new hybrid filter, a combination of the FIR Lagrange interpolator filter and the Thiran allpass IIR filter, is proposed. Methods to reduce the approximation error are discussed.     

基于最大互信息的图像拼接优化算法

基于多分辨分析(MA)策略,提出了以图像最大互信息(MI)为匹配测度的图像拼接粒子群优化算法(OA-MI),使参数随图像的MI计算和多分辨率级数进行自适应调整,解决了灰度图像配准中由于目标函数容易陷入局部极值而造成的误匹配问题。实验证明,该方法能够有效地避免局部极值的影响,通过有限次寻优迭代即可找到最优配准变换,提高了图像配准的计算速度和图像拼接的质量。     

Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.     

LFM信号参数估计的插值FrFT修正算法

针对线性调频（LFM）信号参数估计插值FrFT算法在信噪比较低时性能下降而且针对不同参数估计性能不稳定的问题,提出了一种修正的插值FrFT算法。首先分析了现有插值FrFT算法问题出现的原因,然后定义了分数阶域量化频率,指出当信噪比较低时,若LFM信号初始频率接近分数阶域量化频率点,插值FrFT算法出现反向补偿的概率增大,性能下降。修正的插值FrFT算法改进了插值方向的判决条件以提高噪声免疫力,并通过频移LFM信号初始频率使其不在分数阶域量化频率点附近。最后,对不同初始频率的LFM信号进行仿真,结果表明,修正的插值FrFT算法提高了LFM信号参数估计精度,性能稳定,而计算量并没有明显增加。      

基于离散分数随机变换的双彩色图像加密算法

该文基于离散分数随机变换和线性同余理论,提出一种单通道双彩色图像加密算法。输入的两幅RGB图像转换成相应的索引图像格式,其中一幅2维索引图像被编码为振幅部分,另一幅则被编码为空域相位掩模。分数域相位掩模由线性同余发生器 (LCG) 生成,并将彩色映射矩阵嵌入其中。引入光学幅相调制技术,在不增加光学元件的基础上实现了双彩色图像加密。离散分数随机变换的分数阶和线性同余函数的4个参数作为密钥提高了算法的安全性,对应所有密钥计算了输入图像和解密图像的均方误差。针对唯密文攻击,噪声叠加和抗裁剪性能分别进行了数值模拟,验证了该算法的可行性和有效性。     

Closed-Form Design of Digital IIR Integrators Using Numerical Integration Rules and Fractional Sample Delays

In this paper, the numerical integration rules and fractional sample delays will be used to obtain the closed-form design of infinite-impulse response (IIR) digital integrators. There are two types of numerical integration rules to be investigated. One is Newton-Cotes quadrature rule, the other is Gauss-Legendre integration rule. Although the proposed IIR digital integrators will involve the implementation of fractional sample delays, this problem is easily solved by applying well-documented design techniques of the finite-impulse response Lagrange and IIR allpass fractional delay filters. Several design examples are illustrated to demonstrate the effectiveness of the proposed method     

基于有理四次Hermite插值和PSO的EMD包络线拟合算法

针对经典三次样条插值在EMD分解中存在undershoot现象,模态混叠问题及分段三次Hermite插值不够灵活等问题,提出一种基于有理四次Hermite插值和PSO的EMD包络线算法.该算法利用有理四次Hermite中的形状参数调整曲线形状,并采用粒子群优化算法从曲线簇中找到最优平滑包络线.通过仿真信号实验和非平稳信号实验,表明该方法能够有效克服传统方法带来的undershoot问题,改善模态混叠效应,同时分解后的IMF分量正交性和能量保存度指标亦均优于经典CSI方法和PCHI方法.     

A New Class of Hybrid Particle Swarm Optimization Algorithm

A new class of hybrid particle swarm optimization （PSO） algorithm is developed for solving the premature convergence caused by some particles in standard PSO fall into stagnation. In this algorithm, the linearly decreasing inertia weight technique （LDIW） and the mutative scale chaos optimization algorithm （MSCOA） are combined with standard PSO, which are used to balance the global and local exploration abilities and enhance the local searching abilities, respectively. In order to evaluate the performance of the new method, three benchmark functions are used. The simulation results confirm the proposed algorithm can greatly enhance the searching ability and effectively improve the premature convergence.     

基于混合PSO小波网络的网络异常检测

提出一种用新型的进化学习算法训练的小波神经网络(WNN).这种新型的进化学习算法是基于粒子群算法(PSO)和共轭下降法(CG)提出的.以往,将粒子群算法用于神经网络的训练一般是可行的.因为粒子群算法相比于其他的优化算法,具有相对简单的结构和快速的收敛速度,然而,由于粒子的搜索坍塌速度过快而导致粒子停滞这种潜在的危险.粒子的持续停滞使搜索结果很难达到全局最优,甚至会陷入局部最优.为了克服粒子群算法缺点提出了改进的混合算法.通过对KDD 99数据集的实验表明,利用新型混合算法训练的小波神经网络对于异常检测具有很高的异常检测率并且又较低的误判率.可见,该方法对于网络异常检测是有效的.     

基于粒子群算法的下行CR-NOMA网络资源分配

将非正交多址接入(Non-orthogonal Multiple Access,NOMA)技术应用于认知无线电(Cognitive Radio,CR)次网络,使次用户的信号在功率域叠加,可以进一步提高次网络的吞吐量。为此,将粒子群算法(Particle Swarm Optimization,PSO)应用于底层模式的CR-NOMA网络进行资源分配,并分为子信道分配和功率分配两个步骤。在子信道分配中,使用结合遗传算法思想的粒子群算法提高算法的全局搜索能力。在此基础上,使用基于罚函数的粒子群算法对子信道功率和信道内用户功率进行分配。仿真结果表明,提出的基于粒子群算法的CR-NOMA网络资源分配相比以往算法能获得更高的次网络吞吐量。     

Fractional Order Digital Differentiator Design Based on Power Function and Least squares

In this article, we propose the use of power function and least squares method for designing of a fractional order digital differentiator. The input signal is transformed into a power function by using Taylor series expansion, and its fractional derivative is computed using the Grunwald–Letnikov (G–L) definition. Next, the fractional order digital differentiator is modelled as a finite impulse response (FIR) system that yields fractional order derivative of the G–L type for a power function. The FIR system coefficients are obtained by using the least squares method. Two examples are used to demonstrate that the fractional derivative of the digital signals is computed by using the proposed technique. The results of the third and fourth examples reveal that the proposed technique gives superior performance in comparison with the existing techniques.     

Efficient Design of Discrete Fractional-Order Differentiators Using Nelder–Mead Simplex Algorithm

Applications of fractional-order operators are growing rapidly in various branches of science and engineering as fractional-order calculus realistically represents the complex real-world phenomena in contrast to the integer-order calculus. This paper presents a novel method to design fractional-order differentiator (FOD) operators through optimization using Nelder–Mead simplex algorithm (NMSA). For direct discretization, Al-Alaoui operator has been used. The numerator and the denominator terms of the resulting transfer function are further expanded using binomial expansion to a required order. The coefficients of z-terms in the binomial expansions are used as the starting solutions for the NMSA, and optimization is performed for a minimum magnitude root-mean-square error between the ideal and the proposed operator magnitude responses. To demonstrate the performance of the proposed technique, six simulation examples for fractional orders of half, one-third, and one-fourth, each approximated to third and fifth orders, have been presented. Significantly improved magnitude responses have been obtained as compared to the published literature, thereby making the proposed method a promising candidate for the design of discrete FOD operators.     

基于分数阶谱相减的语音增强法

该文提出了基于分数阶谱相减的语音增强法(FSS)。该方法通过对带噪语音信号作分数阶傅里叶变换(FRFT),将得到的分数阶语噪混合谱与估计的分数阶噪声谱相减,最后利用分数阶Fourier反变换获得去噪后的语音信号。理论分析表明,所提方法存在一个最佳分数阶阶数,使得语噪混合信号能在分数阶变换域得到最好的分离,从而有效地提高了增强语音的性能。计算机仿真表明,对于混有加性白噪声的男/女声发音信号,所提方法在信噪比提高量和Itakura距离减少量两个方面都优于传统的谱相减法(SS),并且增强语音中的音乐噪声得到了明显抑制。     

粒子群优化算法在FIR数字滤波器设计中的应用

本文针对有限脉冲响应(FIR)数字滤波器的设计实质上是一个多参数优化问题,提出了一种用粒子群优化算法(PSO)设计FIR数字滤波器的方法.首先将滤波器的设计问题转化为滤波器参数的优化问题,然后利用粒子群优化算法对整个参数空间进行高效并行搜索以获得参数的最优化.FIR数字低通、带通滤波器设计实例证明了该方法的有效性和优越性.     

Design of IIR digital filters based on eigenvalue problem

This paper presents a new method for designing IIR digital filters with optimum magnitude response in the Chebyshev sense and different order numerator and denominator. The proposed procedure is based on the formulation of a generalized eigenvalue problem by using Remez exchange algorithm. Since there exist more than one eigenvalue in the general eigenvalue problem, we introduce a very simple selection rule for the eigenvalue to be sought for where the rational interpolation is performed if and only if the positive minimum eigenvalue is chosen. Therefore, the solution of the rational interpolation problem can be obtained by computing only one eigenvector corresponding to the positive minimum eigenvalue, and the optimal filter coefficients are easily obtained through a few iterations. The design algorithm proposed in this paper not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue. Some properties of the filters such as lowpass filters, bandpass filters, and so on are discussed, and several design examples are presented to demonstrate the effectiveness of this method     

Multipath channel identification by using global optimization in ambiguity function domain

A new transform domain array signal processing technique is proposed for identification of multipath communication channels. The received array element outputs are transformed to delay-Doppler domain by using the cross-ambiguity function (CAF) for efficient exploitation of the delay-Doppler diversity of the multipath components. Clusters of multipath components can be identified by using a simple amplitude thresholding in the delay-Doppler domain. Particle swarm optimization (PSO) can be used to identify parameters of the multipath components in each cluster. The performance of the proposed PSO-CAF technique is compared with the space alternating generalized expectation maximization (SAGE) technique and with a recently proposed PSO based technique at various SNR levels. Simulation results clearly quantify the superior performance of the PSO-CAF technique over the alternative techniques at all practically significant SNR levels.