On the computation of discrete Legendre polynomial coefficients

A new and fast method to find the discrete Legendre polynomial (DLP) coefficients is presented. The method is based on forming a simple matrix using addition only and then multiplying two elements of the matrix to compute the DLP coefficients.     

非圆孔径离散采样点正交多项式波前拟合

Zernike多项式拟合是一种在光学领域中广泛应用的分析技术.由于现代光学工程中采集数据的离散性和非圆孔径系统的大量使用,Zernike多项式拟合不能完全满足分析需要.提出了一种基于Zernike多项式的非圆孔径离散采样点的正交多项式.通过矩阵的QR分解方法得到在离散采样点上的正交多项式基底.分别使用Zernike多项式和正交多项式对150 mm90 mm的矩形光栅反射波前进行拟合,结果表明两种方法残差波前的PV和RMS值分别相差0.013波长和小于0.001波长.对比不同项数拟合的正交多项式和Zernike多项式系数表明,正交多项式系数之间彼此独立,并由正交多项式系数计算得到了对应的Seidel像差.正交多项式各项系数可以逐项求解,该方法可以显著提高求解速度.     

基于Karhunen-Loeve变换的正交椭圆球面波脉冲波形设计

针对正交椭圆球面波函数(PSWF)脉冲硬件实现复杂度高和难以实时产生的问题,通过对PSWF脉冲求解和正交化两个过程的优化整合,该文提出了一种基于Karhunen-Loeve变换的正交PSWF脉冲波形设计方法。该方法首先将PSWF脉冲表示为Legendre多项式加权求和的形式,通过对原脉冲互相关矩阵进行Karhunen-Loeve变换,得到正交系数矩阵,从而实现PSWF脉冲的正交化。以此为基础,设计了一种高效快捷的正交PSWF脉冲实现方案,建立了正交PSWF脉冲与Legendre多项式系数向量的对应关系,能够通过改变特征多项式的系数来快速设计正交PSWF脉冲,同时具有实时性好和实现复杂度低的优点,为正交PSWF脉冲的工程化实现提供了一种高效快捷的新方案。     

基于勒让德多项式的椭圆球面波脉冲设计方法

针对椭圆球面波函数(PSWF)硬件实现困难的问题,从PSWF与勒让德多项式二者微分方程定义的相似性出发,提出一种基于归一化勒让德多项式的PSWF脉冲设计方法。该方法根据所设计脉冲的时宽和时间带宽积两个参数生成对称矩阵,计算该矩阵的特征向量,得到各阶归一化勒让德多项式的系数,通过归一化勒让德多项式加权求和的方法构建PSWF脉冲。该方法可以通过改变归一化勒让德多项式的系数快速设计不同的PSWF脉冲,具有实时性好、精度可控和硬件复杂度低的优点。     

An algorithm for the computation of the transfer function matrix of generalized two-dimensional systems

A generalized Leverrier's algorithm is developed for the computation of the transfer function matrix of a singular two-dimensional discrete-time system. The algorithm is a recursion in terms of the original system matrices, and does not require the inversion of a polynomial matrix.This research was partially supported by NSF Grant ECS-8518164.     

Stabilising discrete polynomials using spectral factorisation

A simple technique for stabilising discrete polynomials is presented. The technique does not require the roots of the polynomial to be computed but instead uses the familiar spectral factorisation method. If the polynomial has unstable roots, they are automatically reflected back inside the unit circle. Stable polynomials remain unaffected.<>     

Direct solutions of sparse network equations by optimally ordered triangular factorization

Matrix inversion is very inefficient for computing direct solutions of the large sparse systems of linear equations that arise in many network problems. Optimally ordered triangular factorization of sparse matrices is more efficient and offers other important computational advantages in some applications. With this method, direct solutions are computed from sparse matrix factors instead of from a full inverse matrix, thereby gaining a significant advantage in speed, computer memory requirements, and reduced round-off error. Improvements of tea to one or more in speed and problem size over present applications of the inverse can be achieved in many cases. Details of the method, numerical examples, and the results of a large problem are given.     

Improved inversion attacks on nonlinear filter generators

Improved inversion attacks on nonlinear filter generators are proposed with computational complexity equal to O(2^r-m), where r denotes the length of the shift register, and m denotes the largest gap between cells with taps to the filter function or connection polynomial. It is shown that the previously proposed set of design criteria does not prevent the improved inversion attack and an additional criterion is proposed based on the relationship between the positions of taps to the filter function and positions of taps to the connection polynomial     

Approche stochastique de l’analyse de la propagation des erreurs d’arrondi et de données dans les algorithmes numériques

Any result of algorithms provided by a computer always contains an error resulting from floating-point arithmetic round-off error propagation. Furthermore signal processing algorithms are also generally performed with data containing errors. The permutationperturbation method, also known under the name CESTAC (contrôle et estimation stochastique d’arrondi de calcul) is a very efficient practical method for evaluating these errors and consequently for estimating the exact significant decimal figures of any result of algorithms performed on a computer. The stochastic approach of this method, its probabilistic proof, and the perfect agreement between the theoretical and practical aspects are described in this paper.     

Closed-Form Orthogonal DFT Eigenvectors Generated by Complete Generalized Legendre Sequence

In this paper, we propose a new method for deriving the closed-form orthogonal discrete Fourier transform (DFT) eigenvectors of arbitrary length using the complete generalized Legendre sequence (CGLS). From the eigenvectors, we then develop a novel method for computing the DFT. By taking a specific eigendecomposition to the DFT matrix, after proper arrangement, we can derive a new fast DFT algorithm with systematic construction of an arbitrary length that reduces the number of multiplications needed as compared with the existing fast algorithm. Moreover, we can also use the proposed CGLS-like DFT eigenvectors to define a new type of the discrete fractional Fourier transform, which is efficient in implementation and effective for encryption and OFDM.      

Analysis of radiation from a horn with a superquadric aperture

This paper presents an analysis of radiation from a horn with a superquadric aperture, modeled using a cascade of superquadric waveguides. Electromagnetic fields within each waveguide are expressed in terms of a set of orthogonal modes derived from polynomial functions based on a Cartesian coordinate system. The scattering matrix at the horn aperture is obtained by calculating the scattering matrix at each of the waveguide junctions using mode matching, and cascading them appropriately. Radiation patterns corresponding to both x- and y-polarizations of the input excitation are then obtained by integrating the aperture field. The computed numerical results are validated by comparing them with the corresponding results obtained from measurements.     

Estimation of crossover DPD using orthogonal polynomials in fixed point arithmetic

This paper deals with the fixed point implementation of crossover digital predistortion (DPD). The implementation of digital predistortion linearization technique on DSPs poses major challenges, regarding cost, power consumption, speed, precision and volume. Depending on resource availability and design restrictions, fixed-point DSPs may be considered as a suitable solution. Least squares estimation of crossover DPD for multiple-input, multiple-output (MIMO) applications using conventional polynomial models face numerical instability for fixed-point processing. Orthogonal polynomials on the other hand are robust to matrix inversion. Fixed point matrix inversion was implemented using LU decomposition and triangular matrix inversion. This paper examines crossover DPD design for MIMO applications, while using fixed-point arithmetic. It also compares the linearization of 2 × 2 MIMO transmitters in the presence of radio frequency crosstalk using both orthogonal and memory polynomial models. The performance of the two crossover DPDs has been evaluated using a 3GPP standard: orthogonal crossover DPD decreased the measured adjacent channel power ratio of the signal from −42 dBc to −52 dBc.     

A new NLOS error mitigation algorithm in location estimation

In this paper, an effective technique is proposed for locating a mobile station's position when the range measurements are corrupted by non-line-of-sight (NLOS) errors. By linearizing the inequality of range models incorporating NLOS errors and adding loose variables, the method first acquires a preliminary estimation that relies on an initial value. After addressing the effect of linearization error and analyzing the preliminary estimation, a noniterative estimator that does not need an initial value is deduced. The method does not require knowledge of NLOS error statistics. Simulation results indicate that the proposed algorithm can restrain the NLOS errors and improve location accuracy.     

Practical Signal Recovery of WLAN OFDM Signals in the Presence of IQ Imbalance, Phase Noise, and Unknown Channel Frequency Response

We propose two solutions to combat against the IQ imbalance, multipath fading, phase noise, and additive white Gaussian noise in the IEEE 802.11a environment. We show by computer simulations that our proposed least squared (LS) and least mean squared (LMS) solutions outperform, in terms of bit error rate, the solutions in some other papers. Our LMS solution, which does not require matrix inversion, is more computational efficient than our LS solution. Hence, our LMS solution is of practical use.     

A discrete approach to the modeling of power electronic switchingnetworks

An approach to time-domain analysis and modeling of power electronic circuits is described. All circuit components (including active and passive elements) are modeled in a discrete manner by transmission-line sections using the transmission-line modeling (TLM) method. This method requires a fixed system matrix which depends only upon the circuit configuration and time step and not on the switching states of the circuit. Since this method adopts a discrete approach, it provides an exact solution to the discrete model and is stable even for stiff networks. Errors are due to the modeling process only and not to the approximate solution of an approximate calculus model. A simulation on a switched-mode power supply is used to illustrate the modeling method, and the simulated results are compared with measurements     

Estimating the area fraction of geophysical fields frommeasurements along a transect

Methods are presented for estimating the fractional area coverage of geophysical phenomena from measurements taken along a transect. These methods are most useful for assessing potential errors in sampling strategies but may also be used for the analysis of data. The procedure provides a means to compute confidence interval estimates of the true area fraction when the autocovariance function for the geophysical field is known or assumed. Another approach that does not require a priori knowledge of the underlying autocovariance function is described for the special case of linear features modeled as a Poisson line process     

A new data extrapolation algorithm for high resolution ISAR imaging

A new data extrapolation algorithm for high resolution radar imaging is presented. The backscattered data are modeled as an autoregressive process where the prediction coefficients are computed using 1D least-square lattice filters. Unlike the well-known Burg or modified covariance methods, least square lattice modeling yields different prediction coefficients for forward and backward directions. The proposed method does not need to satisfy Levinson recursion, i.e. does not suffer from the limitations of the Burg method such as spectral splitting or bias in the locations of the scattering centers. Moreover, due to its lattice structure it does not need any matrix inversion like the modified covariance method. Results obtained for an experimental target are included to confirm the proposed algorithm.     

A Possible Procedure to Calculate Correlation Functions for the EEG

Usually, the correlation function is obtained by using pure delay elements which are difficult to synthesize on an analog computer. In this paper a calculation procedure which approximates the correlation function by a polynomial is proposed. This procedure, based on an identification method developed by Izawa and Furuta ll, does not require any pure delay element but rather a bank of simple filters.     

米波雷达仰角和多径衰减系数联合估计算法

 针对多径信号严重影响米波雷达低仰角测高的问题,基于广义MUSIC算法的思想,提出了一种可同时估计目标仰角和多径衰减系数的新算法。该算法利用阵列协方差矩阵和搜索角度计算出虚拟的多径衰减系数,然后将该系数与搜索角度一起构造子空间,当该子空间与噪声子空间正交时,即可获得波达方向角度,对应的系数即为多径反射波相对于直达波的多径衰减系数。该算法在克服多径效应的同时,不损失阵列孔径,不要求阵列具有特殊的结构。理论分析和仿真结果表明了该算法的优越性。     

Exact temporal eddy current compensation in magnetic resonance imaging systems

A step-response method has been developed to extract the properties (amplitudes and decay time constants) of intrinsic-eddy-current-sourced magnetic fields generated in whole-body magnetic resonance imaging systems when pulsed field gradients are applied. Exact compensation for the eddy-current effect is achieved through a polynomial rooting procedure and matrix inversion once the 2 N properties of the N-term decay process are known. The output of the inversion procedure yields the required characteristics of the filter for spectrum magnitude and phase equalization. The method is described for the general case along with experimental results for one-, two-, and three-term inversions. The method's usefulness is demonstrated for the usually difficult case of long-term (200-1000-ms) eddy-current compensation. Field-gradient spectral flatness measurements over 30 mHz-100 Hz are given to validate the method.