Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries

In this paper we present a new and numerically efficient technique for designing 2-D linear phase octagonally symmetric digital filters using Schur decomposition method (SDM) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps. First, the 2-D impulse response matrix is decomposed into a parallel realization of k sections, each comprising two cascaded linear phase SISO 1-D FIR digital filters. It is shown that using the symmetry property of the 2-D impulse response matrix and the fact that the left and right eigenspaces obtained by SDM are transpose of each other, the design problem of two 1-D digital filters is reduced to the design problem of only one 1-D digital filter in each section.     

A new design approach for dual‐band patch antenna serving Ku/K band satellite communications

A printed planar antenna with simple and intelligent geometrical structure has been proposed for Ku/K band satellite communication systems. The radiating patch of the antenna is formed by cutting rectangular slots and extending the radiating element to some extent. The final design of the antenna with optimized parameters is fabricated on ceramic–polytetrafluoroethylene substrate materials of dielectric constant ε_r = 10.2. The antenna is excited through a microstrip feed line and has reduced ground plane that covers only the non‐radiating portion of the antenna. The reduced complexity of the antenna is easy to fabricate and has overall dimension of 40 × 35 × 1.905 mm³. The results from experimental analysis show that the proposed antenna can guarantee a wide bandwidth of 12.0 to 16.4 GHz at lower band, and the upper band covers the frequency in the range of 17.53 to 19.5 GHz. The antenna has achieved appreciable gain in the range of 3.14 to 4.68 dBi for lower band and 2.03 to 3.65 dBi for upper band. The proposed antenna has offered almost symmetrical and directional radiation pattern that is essentially suitable for serving Ku/K band satellite applications. Copyright © 2015 John Wiley & Sons, Ltd.     

Aggregation of the policy iteration method for nearly completelydecomposable Markov chains

A steady-state optimal control problem is considered for nearly completely decomposable Markov chains. In order to apply the policy iteration method of R.A. Howard (Dynamic Programming and Markov Processes, Cambridge, MA, MIT Press, 1960), a high-dimensional ill-conditioned system of algebraic equations must be solved in the value-determination step. Although algorithms exist for aggregation of the steady-state probability distribution problem, they only provide methods for computing the cost, not the dual variables. Using a singular perturbation approach, an aggregation method for the value-determination equation is developed. The aggregation method is developed in three steps. First, a class of similarity transformations that transform the system into a singularly perturbed form is developed. Second, an aggregation method to compute the steady-state probability distribution is derived. Third, this aggregation method is applied to the value determination step of Howard's method (1960)     

A real Schur form method for modeling singularly perturbed systems

A method is presented for modeling a two-time-scale system in the singularly perturbed form. The method uses an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form by a transformation into an ordered real Schur form, followed by balancing. Second, under some conditions on the ordered real Schur decomposition, a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables     

Schur Decomposition and Model Reduction in the Design of Two-Dimensional Separable-Denominator Digital Filters

A new and numerically efficient technique for designing two-dimensional (2-D) separable-denominator digital filters using Schur decomposition (SD) and the diagonal symmetry of the 2-D impulse response specifications. This technique is based on two steps: first, the 2-D impulse response specifications are decomposed into two cascaded specifications, representing SIMO and MISO 1-D digital filters. By using the symmetry property of the 2-D impulse response matrix and that the left and right eigenspaces obtained by SD are a transpose of each other, the design problem of the two 1-D digital filters is reduced to the design problem of only one 1-D digital filter. Thus, the computational effort is reduced by approximately half. Further computational reduction is obtained by applying the SD to only part of the 2-D impulse response matrix, the leading principal minor submatrix, and from the symmetry property of the class of filters that are considered here, the decomposition of the impulse response matrix is obtained. In the second step, a model reduction algorithm is used to design a filter that approximates the 1-D specifications obtained from the first step. Two design examples illustrate the advantages of the proposed technique.     

Design of linear-phase IIR digital filters using singularperturbational model reduction

A new technique for the design of a passband linear-phase infinite impulse response (IIR) digital filter is presented. This technique is based on computing orthonormal bases, which span the left and right invariant subspaces associated with the large and small eigenvalues of the cross-Gramian matrix W_c0, which tends to be symmetric and easily constructed. The orthonormal bases are computed by using the ordered real Schur form decomposition, which has been proved to be robust and numerically stable. The proposed technique is illustrated by several examples     

Vehicular emissions and concentrations in school zones: A case study

Recent research has revealed that human exposure to air pollutants such as CO, NO_x, and particulates can lead to respiratory diseases, especially among school-age children. Towards understanding such health impacts, this work estimates local-scale vehicular emissions and concentrations near a highway traffic network, where a school zone is located in. In the case study, VISSIM traffic micro-simulation is used to estimate the source of vehicular emissions at each roadway segment. The local-scale emission sources are then used as inputs to the California line source dispersion model(CALINE4) to estimate concentrations across the study area. To justify the local-scale emissions modeling approach, the simulation experiment is conducted under various traffic conditions. Different meteorological conditions are considered for emission dispersion. The work reveals that emission concentrations are usually higher at locations closer to the congested segments, freeway ramps and major arterial intersections. Compared to the macroscopic estimation(i.e. using network-average emission factors), the results show significantly different emission patterns when the local-scale emission modeling approach is used. In particular, it is found that the macroscopic approach over-estimates emission concentrations at freeways and under-estimations are observed at arterials and local streets. The results of the study can be used to compare to the US environmental protection agency(EPA) standards or any other air quality standard to further identify health risk in a fine-grained manner.