Design of 1-D and 2-D IIR eigenfilters

An effective method is proposed for the design of recursive digital filters in the time/spatial domain. The method is based on the computation of an eigenvalue and its corresponding eigenvector of an appropriate real symmetric and positive-definite matrix derived from the objective error function of the impulse response in the least-squares sense. The method can be used to design 1D IIR digital filters as well as 2D IIR digital filters. The method is easy and the performance is comparable to those of the existing methods. One of the main advantages of the proposed method is that the solution is obtained directly without the need for iteration     

Performance of DMI and eigenspace-based beamformers

The performance of the direct matrix inversion (DMI) method for antenna arrays of arbitrary geometry is analyzed by asymptotic statistical techniques. The effects of eigenspace disturbance caused by finite samples on the output interference and noise powers are examined under the unit gain constraint in the direction of the desired signal. The results show that the performance of the DMI method is degraded mostly by the disturbed noise subspace. That suggests the use of an eigenspace-based beamformer in which the weight vector is computed by using the signal-plus-interference subspace component of the sample correlation matrix. Convergence properties of the eigenspace-based beamformer are evaluated for the cases in which the source number is known and in which it is overestimated. Theoretical analyses validated by computer simulations indicate that the eigenspace-based beamformer has faster convergence rate than the DMI method     

一种实用高效的二维FIR滤波器

本文提出了一个适用的、高效和的二维FIR数字滤波器的设计新方法,此方法的基本原理是冲击响应舍入法,它与传统的设计方法相比,大大地节省了计算时间,提出了效率。文中详细讨论了新滤波器的实用性,并通过在服装逢缝处理皱褶信号获取的信号处理上的应用,证实了它的可行性。     

Scanning Polymeric Waveguide Design of a 2-D Display System

Many small-scale display systems used in head-mounted displays (HMDs) create planar images by beaming light from an optical fiber onto deflectable or rotating mirrors. This mirror-based approach has a critical limitation: the hardware of mirror scanners and grating deflectors must be significantly larger than the light beam diameter to avoid undesirable clipping or diffraction effects. Typically, attempting to reduce the size of a conventional display device reduces pixel count by loss of resolution or field-of-view (FOV) of the device. In this paper, we propose a HMD system utilizing a microfabricated 2D optical scanner controlled by a field-programmable gate array (FPGA) that overcomes the size limitations of other systems while maintaining high resolution.     

Projective analysis of 2-D images

The use of the heatlike equation has been extended to the projective case in order to find a projective analysis of curves and images; unfortunately, this formulation leads to a fifth-order partial differential equation (PDE) that is not easy to implement. Thanks to the use of a three-dimensional (3-D) homogeneous representation of a picture, we present an alternative. Roughly speaking, it is a kind of decomposition of the heatlike formulation with well-posed second-order PDEs. The number of parameters goes from one to three (the scale parameter and two direction parameters). Moreover, this study allows us to propose a simplified multiscale analysis, which is given by an unique PDE (one parameter), for the subgroup of the projective transformations associated, up to a nonzero scalar factor, to an orthogonal 3x3 matrix.     

DESIGN AND ANALYSIS OF MULTI-STEP AMPLITUDE QUANTIZATION WEIGHTED 2-D SOLID-STATE ACTIVE PHASED ARRAY ANTENNAS

An aperture design technique using multi-step amplitude quantization for two-dimensional solid-state active phased arrays to achieve low sidelobe is described. It can be applied to antennas with arbitrary complex aperture. Also, the gain drop and sidelobe degradation due to random amplitude and phase errors and element (or T/R module) failures are investigated.     

Design of 2-D FIR Filters by a Feedback Neural Network

A Hopfield-type neural network for the design of 2-D FIR filters is proposed. The network is contrived to have an energy function that coincides with the sum-squared error of the approximation problem at hand and by ensuring that the energy is a monotonic decreasing function of time, the approximation problem can be solved. Two solutions are obtained. In the first the 2-D FIR filter is designed on the basis of a specified amplitude response and in the second a filter that has specified maximum passband and stopband errors is designed. The network has been simulated with HSPICE and design examples are included to show that this is an efficient way of solving the approximation problem for 2-D FIR filters. The neural network has high potential for implementation in analog VLSI and can, as a consequence, be used in real-time applications.     

Wavelet-based multifractal analysis of 1-D and 2-D signals: New results

During the past decade, new tools stemming from fractal geometry and wavelet analysis are meeting with great success in signal image processing. This paper will focus on these two topics: Wavelets and Multifractal. Both themes evolved towards self contained theories, and yet, a host of reasons justify for coupling them in same applications. It is well known that both analyses share the same conceptual backbone of “scale”: it is the “mathematical zoom” commonly associated to wavelet analysis and it is the “scaling laws” that underlie multifractal structures. Very naturally then, wavelets stood as a privileged tool for analyzing and characterizing multifractal signals and images. Hence, the purpose of this paper is to illuminate some of the issue involved in taking advantage of the current advances in wavelets and multifractals analysis. We discuss continuous, discrete, orthogonal wavelets and present applications to fracture processes and medical ultrasound imaging.     

Design of a low-cost 2-D beam-steering antenna using ferroelectricmaterial and CTS technology

The design of a new low-cost antenna array with two-dimensional beam-scanning capability is presented in this paper. The design procedure is based on the continuous transverse stub (CTS) technology and the use of ferroelectric material. With the application of a low-loss ferroelectric material barium strontium titanium oxide with 40% oxide III, beam-scan capability from -60° to 60° was achieved. The tradeoffs in selecting the ferroelectric material and between losses and bias voltage in the CTS design were also examined. Furthermore, it was found necessary to adjust the dimensions of the radiating stubs, as well as the connecting sections of the feed waveguide so as to eliminate reflections between the stubs and, hence, maintain the desirable radiation pattern. It is shown that the use of an average height for the feed waveguide will result in deterioration in the radiation pattern     

Stability analysis of linear 2-D systems

The present paper is concerned with stability analysis of linear two-dimensional systems described by Fornasini–Marchesini state-space model. Necessary and sufficient conditions for asymptotic stability of the systems are obtained first. Several simple stability criteria are derived via the nonnegative matrix theory, which are sharper than those in literature. When all the parameter matrices are nonnegative, the criteria are necessary and sufficient for stability of the system. Illustrative examples are provided.     

Quadratic Regularization Design for 2-D CT

Statistical methods for tomographic image reconstruction have improved noise and spatial resolution properties that may improve image quality in X-ray computed tomography (CT). Penalized weighted least squares (PWLS) methods using conventional quadratic regularization lead to nonuniform and anisotropic spatial resolution due to interactions between the weighting, which is necessary for good noise properties, and the regularizer. Previously, we addressed this problem for parallel-beam emission tomography using matrix algebra methods to design data-dependent, shift-variant regularizers that improve resolution uniformity. This paper develops a fast angular integral mostly analytical (AIMA) regularization design method for 2-D fan-beam X-ray CT imaging, for which parallel-beam tomography is a special case. Simulation results demonstrate that the new method for regularization design requires very modest computation and leads to nearly uniform and isotropic spatial resolution in transmission tomography when using quadratic regularization.     

The statistical performance of eigenspace-based adaptive arraybeamformers

We analyze the statistical performance of several eigenspace-based adaptive array beamformers, including conventional direct-form beamformers and generalized sidelobe canceler (GSC). It is shown that the convergence rate of eigenspace-based adaptive array beamforming depends on the number of array elements, the input signal-to-noise ratio (SNR), and the number of interferers when the desired signal is present during the weight adaptation. In contrast, the misadjustment of the array output power is a function of the number of interferers and is independent of the number of array elements when the desired signal is absent. Several simulation examples are also provided to confirm the theoretical results     

二维DCT算法及其精简的VLSI设计

采用了快速算法,并通过矩阵的变化,得到了一维离散余弦变换(Discrete Cosine Transform,DCT)的一种快速实现,并由此提出一种精简的超大规模集成电路(Very-large-scale integration,VLSI)设计架构.使用了一维DCT的复用技术,带符号数的乘法器设计等技术,实现了二维DCT算法的精简的VLSI设计.实验结果表明,所设计的二维DCT设计有效,并能够获得非常精简的电路设计.     

基于 RMA 的三维成像与二维 MIMO 阵设计

距离迁移(RM)算法能够精确校正近场距离徙动,同时通过使用快速傅里叶变换可以达到很高的计算效率,具有应用于近场MIMO雷达三维实时成像的潜力。RM算法应用于近场MIMO成像的主要挑战是设计合适的阵列结构。文中利用球面波分解为无穷多个平面波的方法推导了MIMO雷达近场三维RM 成像算法,在深入分析算法实现流程的基础上得 到了RM算法对MIMO阵列构型的四条约束条件。提出了一种适用RM算法的MIMO阵列设计方法,并利用所提方法设计了MIMO阵列,结合仿真,分析了所设计阵列的成像性能。     

Lyapunov stability analysis of higher-order 2-D systems

In this paper we prove a necessary and sufficient condition for the asymptotic stability of a 2-D system described by a system of higher-order linear partial difference equations. We show that asymptotic stability is equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four-variable polynomial algebra.     

2-D FFT algorithm by matrix factorization in a 2-D space

A new 2-D FFT algorithm is described. This algorithm applies a 2-D matrix factorization technique in a 2-D space and offers a way to do 2-D FFT in both dimensions simultaneously. The computation is greatly reduced compared to traditional algorithms. This will improve the realization of a 2-D FFT on any kind of computer. However its good parallelism will especially benefit an implementation on a computer with hypercube architecture. A good arrangement of parallel processors will save a great deal of running time. Furthermore this algorithm can be extended toM-D cases forM>2.Supported by NSF Grant CCR-8813493.Supported by Grants DMS-8607687, DMS-8722402, and DMS9002019.     

二维线性相位FIR数字滤波器的优化设计

该文提出了一种用神经网络算法来设计二维线性相位数字滤波器的新方法。通过分析二维FIR线性相位滤波器的幅频响应特性,建立了神经网络算法。根据给定的幅频响应指标,按该算法可获得滤波器系数。为保证该算法的稳定性,提出并证明了该算法的收敛定理。文中给出了圆对称和矩形对称二维低通线性相位FIR数字滤波器优化设计实例。计算机仿真结果表明由该方法设计的二维数字滤波器,通带和阻带范围波动小,所需计算量非常少,稳定性强,因而是一种优异的设计方法。     

Automated 2-D cephalometric analysis on X-ray images by a model-based approach

Craniofacial landmark localization and anatomical structure tracing on cephalograms are two important ways to obtain the cephalometric analysis. In order to computerize them in parallel, a model-based approach is proposed to locate 262 craniofacial feature points, including 90 landmarks and 172 auxiliary points. In model training, 12 landmarks are selected as reference points and used to divide every training shape to 10 regions according to the anatomical knowledge; principle components analysis is employed to characterize the region shape variations and the statistical grey profile of every feature point. Locating feature points on an input image is a two-stage procedure. First, we identify the reference landmarks by image processing and pattern matching techniques, so that the shape partition is performed on the input image. Then, for each region, its feature points are located by a modified active shape model. All craniofacial anatomical structures can be traced out by connecting the located points with subdivision curves according to the prior knowledge. Users are permitted to modify the results interactively in many different ways. Experimental results show the advantage and reliability of the proposed method.     

Stability analysis for a class of complex dynamical networks with 2-D dynamics

In this paper, the problems of stability and decentralized control are studied for a class of linear coupled dynamical networks with Fornasini–Marchesini second local state-space dynamics. Necessary and sufficient stability conditions are obtained for a class of linear network composed by $N$ identical nodes. Effects of the interconnection on stability of network are presented by eigenvalues of the topological matrix, and the effectiveness of interconnection on network stability is pointed out. Moreover, the decentralized control laws are presented for two types of linear regular networks: star-shaped coupled networks and globally coupled networks in detail. The relationships between the stability of a network and the stability of its corresponding nodes are studied. It is shown that some nodes must be made stable in order to stabilize the whole network in some cases. However, the detailed relationship is needed to be further investigated.     

Design of a fully-pipelined systolic array for flexible transposition-free VLSI of 2-D DFT

A novel approach to design an efficient systolic structure to implement the two-dimensional discrete Fourier transform (DFT) is presented. The proposed systolic structure consists of (N/spl times/N) simple locally connected processing elements that perform two complex multiplications and two additions during a cycle period. It does not involve any transposition operation and, therefore, the corresponding hardware and time is saved by the structure. It offers full pipelining, and computes a two-dimensional DFT of size (N/spl times/N) in every N cycles without interruption, since the first stage of operations for one input array may be performed concurrently with second stage of operations of its preceding input array.