Some new results on stability robustness of two-dimensional discrete systems

In this paper, we study the problem of stability robustness of two-dimensional discrete systems in a local state-space setting. Two methods are proposed for efficient numerical evaluation of the exact complex perturbation bound . The first method combines Byers' bisection method with a three-point-pattern optimization technique to compute . The second method utilizes a direct optimization technique to find the bound. In addition, a 2-D Lyapunov approach is proposed to obtain two lower bounds of , and numerical techniques for solving the constant 2-D Lyapunov equation involved are presented. The paper is concluded with an example illustrating the main results obtained.     

Reflection and transmission characteristics of a slab with periodically varying surfaces

Using a plane wave spectral decomposition of the relevant electromagnetic (EM) fields and the T-matrix solution philosophy, a T-matrix is formulated which completely characterizes the EM response of an infinite material plate bounded by two homogeneous half-spaces, the two interfaces being periodically rough. Individual T-matrices for either of the two periodic bimaterial interfaces are used in this derivation. Using the computed results, the anomalies in the scattering response of the rough slab are explained in terms of reflectionless and transmissionless modes, the Brewster angle, and the conditions for propagation or evanescence of a given plane wave mode.     

Some results on sensitivity of general input-output systems

We consider general input-output systems, which need not be of a feedback type, that are governed by nonlinear operator equations which relate the input, state, and output. Assuming that these equations depend on a parameterA which is allowed to vary in a neighborhood of a nominal valueA ₀ , we study the dependence of the output onA when the input is fixed. Essentially, we call a system insensitive if the output depends continuously onA. Two insensitivity concepts are introduced, and it is shown that certain monotonicity-like conditions ensure insensitivity. Also, several particular cases of the governing equations are studied. As examples, a control system described by a singular system of ordinary differential equations and a nonlinear feedback system are discussed.     

Some results on robust stability of general input-output systems

We consider general input-output systems governed by nonlinear operator equations that relate the system's input, state, and output. The systems under consideration need not be of a feedback type. Assuming that the governing equations depend on a parameterA in a linear space that is allowed to vary in a vicinity N_r(A₀) of a nominal valueA ₀, we study conditions under which the system is stable for each AN_r (A₀), i.e., when the system is robust. By stability we essentially mean that the input-output map is continuous. Depending on the type of continuity used, two concepts of robustness are introduced. The main theorem shows that a certain generalized monotonicity condition imposed on the nominal system combined with a Lipschitz-like condition imposed on the perturbed system guarantees robustness. Moreover, several particular cases of the governing equations are investigated. As examples, we consider (1) a singular system of nonlinear ordinary differential equations (a semistate equation), (2) a feedback system, and (3) a feedback, feedforward system. At the end of this paper some extensions and modifications of the presented theory are discussed.     

Some new results on binary linear block codes

Certain properties of the parity-check matrix H of (n, k) linear codes are used to establish a computerised search procedure for new binary linear codes. Of the new error-correcting codes found by this procedure, two codes were capable of correcting up to two errors, three codes up to three errors, four codes up to four errors and one code up to five errors. Two meet the lower bound given by Helgert and Stinaff, and seven codes exceed it. In addition, one meets the upper bound. Of the even-Hamming-distance versions of these codes, eight meet the upper bound, and the remaining two exceed the lower bound.     

Some experimental and modeling results of widely varying urban environments on train mobile radio communication

A comparative study of urban mobile radio wave propagation characteristics in the UHF band has been carried out based on the field strength measurements conducted inside a moving train in two widely varying urban environments. Various prediction techniques are employed to compare the observed path losses with those of predicted ones in both the environments. The major fall out of the present study is the modification of Xia's model, which gave better agreement with the observed results. The deviations of the prediction techniques and their suitability have been discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Some results and insights on the performance gains of MIMO systems

Multiple-input-multiple-output (MIMO) systems generally fall into two categories, depending on the kind of gain they provide: spatial multiplexing (SM) methods yield capacity gain and diversity methods yield link quality gain [measured here by the post-processing signal-to-noise ratio (SNR)]. We consider a set of systems from each category, quantify their gains analytically or via simulations, and show how these gains vary with the receiver input SNR and the numbers of antennas. The contribution of this work resides in both the closed-form analytical results and the numerical comparisons. We both highlight the benefits of using additional transmit antennas and provide comparisons among diversity-based and SM-based MIMO schemes. The analytical results are for a diversity-based scheme that combines selection diversity at the transmit side with maximum ratio combining (MRC) at the receive side, which we show to upper bound the SNR performance of other diversity-based schemes. We find that, for practical system parameters, the relevant SNR metric is 6-12 dB higher for the diversity-based schemes than for SM-based schemes. At the same time, SM-based schemes yield capacity metrics which range from 30% higher to double that of diversity-based schemes.     

Application of the impedance sheet concept to thin periodically varying dielectrics

The impedance sheet concept used to predict the transmission and reflection properties of thin dielectrics is extended to determine the transmission and reflection properties of thin periodically varying dielectrics. For plane-wave incidence, the effect of the periodic interface is to generate a higher order modal distribution on both sides of the boundary. It is shown that situations exist where the higher order modes can be strongly excited, and in fact can carry more power than the dominant transmitted mode. The frequency response of the dielectric is obtained and shown to be quite different than the homogeneous thin dielectric except at lower frequencies.     

Some new results of IR systems' sensitivity equations

Typical IR systems' sensitivity equations have been established for decades, these include the NETD equation for IR imaging systems, and the acquisition and tracking range equations for IR searching and tracking systems, but they only fit the specific or simplified conditions. For example, the NETD equation can only be used for systems tested under the standard condition. In the field application, we must deal with the noise equivalent radiance difference NELD, not the NETD, and give out its explicit equation for concrete calculation. For the range equation, when the small target, often called a point source, is not strong enouph, i. e., when the target contrast is seriously decreased, we must consider the unneglectable background effect. In this paper, we summarrize some more general and valuable IR systems' sensitivity equations, which can be used for the practical engineering analysis and projection effectively.     

Random-access systems with a time varying channel

A random multiple-access system which employs a collision resolution algorithm for accessing a common time-varying channel is considered. The channel is assumed to be in one of two states. In each state, the channel is characterized by a general discrete memoryless channel and the transitions between the two states are assumed to be Markovian. A set of sufficient conditions for the ergodicity (stability) of the system is established. As an example, the case when the Capetanakis tree algorithm operates with a time-varying noisy channel is examined. The stability of this system is analyzed, and the throughput is evaluated     

Circuit theory of periodically driven nonlinear systems

The systems under discussion are nonlinear, but driven by a strong periodic "carrier." Examples of such systems are oscillators, frequency multipliers, limiters, modulators, and periodically driven feedback systems. It is of interest to inquire how small perturbations on the periodic driving are propagated throughout the system, and to this end a circuit theory for these perturbations is developed. In different Contexts these perturbations could be desired or undesired modulation, noise, hum, or synchronizing signals. In general the random processes in such a system will, because of the periodic driving, be nonstationary; but various representations are developed that are stationary, and hence can be described by spectral analysis. The concept of impedance is developed for the small perturbations, and the validity of Kirchhoff's Laws is examined. Specific problems are not treated in detail; instead, a general framework is set up within which a variety of problems can be analyzed. Problems of this sort include the theory of noise in oscillators, propagation of noise and modulation in nonlinear systems, the noise theory of frequency multipliers, and synchronization of oscillators.     

Interaction between an electron beam of periodically varying diameter and EM waves in a cylindrical guide

A simple theory is presented of forward and backward wave interaction between a fast wave in a guide and an electron beam injected into a magnetic field and rippling at the cyclotron frequency. Experiments on a tube at Q band seem to confirm the theory but show that there are other effects as well. An RF output of 36 kW in the forward wave mode indicates a possible traveling wave amplifier at millimeter wavelengths.     

Some new results on propagation of electromagnetic waves in strongly turbulent media

New results for the covariance of the intensity fluctuations of a plane wave propagating in a strongly turbulent medium are presented, and the consequences of these new results on aperture averaging, angle of arrival fluctuations, and the temporal frequency spectrum of the intensity scintillations are evaluated. The differences between the strong turbulence and weak turbulence cases are generally quite significant.     

Representations of linear periodically time-varying and multirate systems

The linear switched time-varying (LSTV), polyphase (blocked), and alias-component representations of linear periodically time-varying (LPTV) systems are studied. In particular, alias-components are related to the time-shifted versions of the system. It is shown that in general, a filterbank is equivalent to the cascade connection of two LPTV systems. By generalizing some of the results of the LSTV representation of LPTV systems, it is shown that for relatively coprime integers p and m, a p-channel filterbank that has LPTV filters with period m is equivalent to an mp-channel filterbank with LTI filters. The representation of multirate systems that have LPTV kernels is discussed next. Due to the presence of the upsampler and downsampler, there are some degrees of freedom in the choice of the kernel. This redundancy is dealt with by choosing from various subclasses so that there is a one-to-one relationship between a multirate system and its kernel. Then, we find the LPTV kernel that has the least period.     

Transmission performance analysis of a new class of line codes for optical fiber systems

A family of mB(m+1)B binary, nonalphabetic, balanced line codes is presented that is suitable for high bit rate (>or=135 Mb/s) optical fiber transmission due to its relatively simple encoding and decoding rules. Here, B represents a block of m bits, where m is an odd number. The coding, decoding, and bit error rate (BER) performance of the codes are discussed. Statistical and spectral analysis for the specific case in which the number of bits, m, equals seven, is presented. This makes possible a detailed comparison of the proposed code with conventional 7B8B codes.<>     

对一个新的平方混沌类的研究

该文提出一个新的平方混沌类,计算了混沌类的李雅普诺夫指数,并对混沌类中结构III所表现出的环面破裂产生混沌和倍周期分岔产生混沌的现象进行了初步的研究,在同一个系统中可以观察到环面破裂和倍周期分岔两种不同的通向混沌的路线,这尚属首次报道。     

A new class of biorthogonal wavelet systems for image transformcoding

We construct general biorthogonal Coifman wavelet systems, a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair. A time-domain design method is employed and closed-form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived. The resulting filter coefficients are all dyadic fractions, which is an attractive feature in the realization of multiplication-free discrete wavelet transform. Even-ordered systems in this family are symmetric, which correspond to linear-phase dual filters. In particular, three filterbanks (FBs) in this family are systematically verified to have competitive compression potential to the 9-7 tap biorthogonal wavelet FB by Cohen et al. (1992), which is currently the most widely used one in the field of wavelet transform coding. In addition, the proposed FB's have much smaller computational complexity in terms of floating-point operations required in transformation, and therefore indicate a better tradeoff between compression performance and computational complexity.     

Analysis of 2-D state-space periodically shift-variant discrete systems

Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.This work was supported in part by a grant from the Colorado Advanced Software Institute.     

On the realization of a class of time varying impulse response matrix

An algorithm for determining a nonminimal time varying realization from a given class of impulse response matrix is proposed. The procedure is based on the techniques of Glass and Lal et al. proposed earlier for time invariant case. The modifications for time varying case are pointed out and the procedure illustrated by an example.