Dual series solution to the scattering of plane waves from a binaryconducting grating

The problem of scattering of electromagnetic waves from a perfectly conducting grating with a periodic groove structure is considered. A system of dual series equations is derived by enforcing the electromagnetic boundary conditions; this leads to a boundary-value problem that is solved. The mathematics leading to the solution of the dual series system is derived from the equivalent Riemann-Hilbert problem in complex-variable theory and its solution. The solution converges absolutely and makes it possible to obtain analytical results, even where other numerical methods, such as the mode-matching method and spectral iteration methods, are numerically unstable. Consideration is also given to the relative phase values for the diffracted fields. The phase differences between the scattered fields resulting from two orthogonally polarized incident plane waves can be explicitly determined for any incidence angles and for any groove dimensions. Comparisons with results from the mode-matching method and the spectral-iteration method are also presented     

A two-phase algorithm and performance bounds for the star-starconcentrator location problem

The introduction of concentrators in a centralized telecommunication network provides a cost-effective way to connect the network. The star-star (SS) network model is considered, and the star-star concentrator location problem (SSCLP) is then examined. The SSCLP is NP-complete and can be formulated as a 0-1 integer programming problem. A two-phase algorithm is developed to solve the SSCLP. In the first phase, dualizing the side constraints produces a Lagrangian problem that is easy to solve and has an optimal value that is a lower bound (for minimization problems) on the optimal value of the original SSCLP. Heuristics then are applied to produce an upper bound (feasible solution) to the SSCLP. In the second phase, a branch-and-bound method is used to refine the solution space to obtain a tighter lower bound. First, an enumeration heuristic is applied to improve the best feasible solution obtained from the first phase. Then, a procedure for deriving bounding problems is presented and various branching strategies are discussed. Computational examples with up to 100 terminals and 30 potential concentrators are considered. All the network designs obtained are shown to be within 2% of optimal     

On the existence of the solution for one-dimensional discrete phase retrieval problem

We consider the discrete form of the one-dimensional phase retrieval (1-D DPhR) problem from the point of view of input magnitude data. The direct method can provide a solution to the 1-D DPhR problem if certain conditions are satisfied by the input magnitude data, namely the corresponding trigonometric polynomial must be nonnegative. To test positivity of a trigonometric polynomial a novel DFT-based criterion is proposed. We use this DFT criterion for different sets of input magnitude data to evaluate whether the direct method applied to the 1-D DPhR problem leads to a solution in all explored cases.     

A novel phase unwrapping method based on network programming

Phase unwrapping is the reconstruction of a function on a grid given its values mod 2π. Phase unwrapping is a key problem in all quantitative applications of synthetic aperture radar (SAR) interferometry, but also in other fields. A new phase unwrapping method, which is a different approach from existing techniques, is described and tested. The method starts from the fact that the phase differences of neighboring pixels can be estimated with a potential error that is an integer multiple of 2π. This suggests the formulation of the phase unwrapping problem as a global minimization problem with integer variables. Recognizing the network structure underlying the problem makes for an efficient solution. In fact, it is possible to equate the phase unwrapping problem to the problem of finding the minimum cost flow on a network, for the solution of which there exist very efficient techniques. The tests performed on real and simulated interferometric SAR data confirm the validity of the approach     

Estimating the orientation of planar surfaces: algorithms andbounds

This paper presents a computationally and statistically efficient parametric solution to the problem of estimating the orientation in space of a planar textured surface from a single, noisy, observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinusoid whose frequency is a function of location. The functional dependence of the sinusoid phase in location is uniquely determined by the tilt and slant angles of the surface. From the physical model of the perspective projection, we derive the Cramer-Rao lower bound on the error variance of estimating the tilt and slant of the observed surface in the presence of observation noise. It is shown in this paper that the phase of each of the sinusoids can be expressed as a linear function of some variables that are related to the surface tilt and slant angles. Using the phase differencing algorithm, we fit a polynomial phase model to a sinusoidal component of the observed texture. Substituting in the derived linear relation, the unknown phase with the one estimated using the phase differencing algorithm, we obtain a closed-form, analytic, and computationally efficient solution to the problem of estimating the tilt and slant angles. The algorithm performance is shown to be close to the Cramer-Rao bound, even for low signal-to-noise ratios, at computational complexity which is considerably lower than that of any existing algorithm     

Phase unwrapping of MR phase images using Poisson equation

The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images. The method is based on the assumption that the magnitude of the inter-pixel phase change is less than pi per pixel. Therefore, the authors obtain an estimate of the phase gradient by "wrapping" the gradient of the original phase image. The problem is then to obtain the absolute phase given the estimate of the phase gradient. The least-squares (LS) solution to this problem is shown to be a solution of the Poisson equation allowing the use of fast Poisson solvers. The absolute phase is then obtained by mapping the LS phase to the nearest multiple of 2 K from the measured phase. The proposed technique is evaluated using MR phase images and is proven to be robust in the presence of noise. An application of the proposed method to the 3-point Dixon technique for water and fat separation is demonstrated.     

Algebraic multidimensional phase unwrapping and zero distributionof complex polynomials-characterization of multivariate stablepolynomials

We define the multidimensional unwrapped phase for any finite extent multidimensional signal that may have its zero on the distinguished boundary of the unit polydisc. By using this definition, we deduce that multivariate stable polynomials can be simply characterized in terms of the proposed unwrapped phase. A rigorous symbolic algebraic solution to the exact phase unwrapping problem for multidimensional finite extent signals is also proposed. This solution is based on a newly developed general Sturm sequence and does not need any numerical root finding or numerical integration technique. Furthermore, it is shown that the proposed algebraic phase unwrapping algorithm can be used to determine the exact zero distribution of any univariate complex polynomial without suffering the so-called singular case problem     

Automated analysis of phased-mission reliability

A method for automated analysis of phased mission reliability which considers the problem in terms of the construction of a continuous-time discrete-state Markov model and uses a standard Markov-chain solution technique that is adapted to the problem of phased missions is presented. The resulting state space is the union of the states in each independent phase, rather than the sum. This results in a model that can be substantially smaller than those required by other methods. A unified framework which is used for defining the separate phases using fault trees and for constructing and solving the resulting Markov model is discussed. The usual solution technique is altered to account for the phased nature of the problem. The framework is described for a previously published, simple three-component, three-phase system. An example in which a hypothetical two-phase application involving a fault-tolerant parallel processor is considered is given. The approach applies where the transition rates (failure and repair rates) are constant and where the phase change times are deterministic     

Computing the Average Symbol Error Probability of the MPSK System Having Quadrature Error

When quadrature error exists, the shape of the M‐ary phase shift keying (MPSK) signal constellation becomes skewed‐elliptic. Each MPSK symbol takes on a different symbol error probability (SEP) value. The analytical results presented thus far have been derived from studies which examined the SEP problem assuming that the SEP of each MPSK symbol is equally likely; therefore, those results should not be treated as offering a complete solution. In this letter, we present a new and more complete solution to the SEP problem of MPSK by relaxing the above assumption and finding the expressions for the average as well as individual SEP in the presence of quadrature error.     

Synthesis of low-peak-factor signals and binary sequences with low autocorrelation (Corresp.)

This correspondence considers the problem of how to adjust the phase angles of a periodic signal with a given power spectrum to minimize its peak-to-peak amplitude. This "peak-factor problem" arises in radar, sonar, and numerous other applications. However, in spite of the wide-spread interest it has evoked, the peak-factor problem has so far defied solution except in cases where the number of spectral components is small enough to permit an effectively exhaustive search of all phase angle combinations. In this correspondence, a formula for the phase angles is derived that yields generally low peak factors, often comparable to that of a sinusoidal signal of equal power. A formula is also derived for the case in which the phase angles are restricted to 0 andpi. The latter formula is applicable to the problem of constructing binary sequences of arbitrary length with Iow autocorrelation coefficients for nonzero shifts.     

基于FFT的相位差测量及虚拟相位差计的实现

本文介绍了一种基于FFT谱分析法分析相位差的方法,即通过提取基波参数,求取被测信号的相位差。相位差的求取在分析系统动态特性时具有重要的意义,如何准确的计算出两信号的相位差是本文研究的重点。本文提出了提高相位差测试精度的方法以及如何解决整周期采样的问题。应用图形化编程语言LabVIEW实现算法仿真,大大减少了程序的开发时间,具有较强的可读性。该算法实现简单、测试精度高。仿真计算验证了算法的有效性,为系统频率特性的研究提供了坚实的理论基础。     

Synthesis of the radiation pattern with specified 3D contour of the main lobe in antenna arrays with complex control

The problem of the matrix synthesis of an antenna array with complex control with the use of a generalized energy functional is solved. It is shown that the proposed solution of the synthesis problem is more general than well-known solutions and enables formation of a specified array complex pattern with required shape of the main lobe with consideration for local requirements on the phase pattern of the antenna array. Results of a numerical experiment performed by the example of a multielement antenna array with complex control, which confirm potentialities of the synthesis method, are presented.     

Greedy randomized adaptive search procedure for analog test point selection

Analog test point selection (ATPS) is an important problem that arises in the area of analog system testing. This paper formulates the problem as a combinatorial problem and proposes a solution method based on greedy randomized adaptive search procedure (GRASP). The proposed method is an iterative procedure, with each iteration consisting of two phases. The first phase, a construction phase, produces a feasible solution. The second, a local search, seeks for improvement on construction solution. In addition to applying the basic GRASP, the algorithm introduces randomness into both phases including: randomizing the selection of greedy criteria and checking redundant test points in a random order. The former can prevent the algorithm from converging prematurely to local optima, while the latter make the algorithm probably get more than one best solution. The efficiency of the proposed method is proven by two practical analog circuits as well as statistical experiments. Results show that our algorithm, compared with other methods, finds the global minimum set of test points more accurately and more efficiently. Therefore, it is a good solution to optimize ATPS.     

Chebyshev approximation of recursive digital filters having specified amplitude and phase characteristics

The design of an IIR filter of prescribed amplitude and phase characteristics can be reduced to an approximation problem for complex valued functions. An algorithm for the solution of this problem is given and some numerical results are presented.     

A novel adaptation of the Michelson interferometer for themeasurement of vibration

An adaptation of the Michelson interferometer for vibration measurement is described. Two outputs are provided, the phases of which can be independently controlled. The device provides a simple low cost solution to the problem of vibration measurement where the direction of the surface velocity is required. The relative phase of the two outputs is controlled without using any moving parts or electronic elements. The ability of the system to track vibration is demonstrated     

Subpixel estimation of shifts directly in the Fourier domain.

In this paper, we establish the exact relationship between the continuous and the discrete phase difference of two shifted images, and show that their discrete phase difference is a two-dimensional sawtooth signal. Subpixel registration can, thus, be performed directly in the Fourier domain by counting number of cycles of the phase difference matrix along each frequency axis. The subpixel portion is given by the noninteger fraction of the last cycle along each axis. The problem is formulated as an overdetermined homogeneous quadratic cost function under rank constraint for the phase difference, and the shape constraint for the filter that computes the group delay. The optimal tradeoff for imposing the constraints is determined using the method of generalized cross validation. Also, in order to robustify the solution, we assume a mixture model of inlying and outlying estimated shifts and truncate our quadratic cost function using expectation maximization.     

Peak-to-RMS reduction of speech based on a sinusoidal model

A sinusoidal-based analysis/synthesis system is used to apply a radar design solution to the problem of dispersing the phase of a speech waveform. Unlike conventional methods of phase dispersion, this solution technique adapts dynamically to the pitch and spectral characteristics of the speech, while maintaining the original spectral envelope. The solution can also be used to drive the sine-wave amplitude modification for amplitude compression, and is coupled to the desired shaping of the speech spectrum. The proposed dispersion solution, when integrated with amplitude compression, results in a significant reduction in the peak-to-RMS (root-mean-square) ratio of the speech waveform with acceptable loss in quality. Application of a real-time prototype sine-wave preprocessor to AM radio broadcasting is described     

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison     

Modular solution of dynamic multi-phase systems

Binary Decision Diagram (BDD)-based solution approaches and Markov chain based approaches are commonly used for the reliability analysis of multi-phase systems. These approaches either assume that every phase is static, and thus can be solved with combinatorial methods, or assume that every phase must be modeled via Markov methods. If every phase is indeed static, then the combinatorial approach is much more efficient than the Markov chain approach. But in a multi-phased system, using currently available techniques, if the failure criteria in even one phase is dynamic, then a Markov approach must be used for every phase. The problem with Markov chain based approaches is that the size of the Markov model can expand exponentially with an increase in the size of the system, and therefore becomes computationally intensive to solve. Two new concepts, phase module and module joint probability, are introduced in this paper to deal with the s-dependency among phases. We also present a new modular solution to nonrepairable dynamic multi-phase systems, which provides a combination of BDD solution techniques for static modules, and Markov chain solution techniques for dynamic modules. Our modular approach divides the multi-phase system into its static and dynamic subsystems, and solves them independently; and then combines the results for the solution of the entire system using the module joint probability method. A hypothetical example multi-phase system is given to demonstrate the modular approach.     

Hierarchical network flow phase unwrapping

The well-studied interferometric synthetic aperture radar (InSAR) problem for digital elevation map generation involves the derivation of topography from the radar phase. The topography is a function of the full phase, whereas the measured phase is known modulo 2/spl pi/, necessitating the process of recovering full phase values via phase unwrapping. This mathematical process becomes difficult through the presence of noise and phase discontinuities. This paper is motivated by research which models phase unwrapping as a network-flow minimization problem. A major limitation is that often a substantial computational effort is required to find solutions. Commonly, these phase images are huge (/spl Gt/10 million pixels), and obviously the sheer size of the problem itself makes phase unwrapping challenging. This paper addresses the development of a computationally efficient hierarchical algorithm, based on a "divide-and-conquer" approach. We have shown that the phase-unwrapping problem can first be partitioned into independent phase-unwrapping subproblems, which can further be recombined to produce the unwrapped phase. Interestingly, the recombination step itself can be interpreted as an unwrapping problem, for which a modified network-flow solution applies! In short, this paper develops a parallelization of the network-flow algorithm, allowing images of virtually unlimited size to be unwrapped and leading to dramatic decreases in the algorithm execution time.