A behavioral interpretation of Liv?ic systems

In the behavioral approach to (discrete-time) multidimensional linear systems, one views solution trajectories simply as the set of all solutions of a homogeneous linear system of difference equations. In this setting the Oberst transfer matrix is identified as the unique rational matrix function H satisfying Q = PH where R =? [?Q P] is a partitioning of the kernel representation R for the behavior such that P has full column rank equal to the rank of R. This Oberst transfer matrix can be seen as a more fundamental and unifying formalism capturing the transfer functions associated with the older Givone-Roesser and Fornasini-Marchesini input/state/output approaches to multidimensional linear systems. A quite different type of input/state/output linear system having original motivation from operator theory is the Liv?ic linear system, where the state-evolution equations are overdetermined and lead to compatibility constraints on the input and output signals; the result is that the admissible input signals are not free but form their own nontrivial behavior. The main point of the present work is to identify how Liv?ic systems fit into the behavioral framework. In particular, we extend the Oberst transfer matrix to the setting of autonomous behaviors lacking any free variables (in which case the standard Oberst transfer matrix is trivial with no columns) by letting the reduced ring (the quotient of the polynomial ring by the behavior-annihilator ideal) act on the behavior. We then make explicit identifications between the Oberst transfer matrix over the reduced ring and the Liv?ic Joint Characteristic Function.     

The discrete multidimensional MPUM

Given a finite set of polynomial-exponential, multivariate, and vector-valued sequences, we show how the smallest linear shift-invariant set containing the data trajectories can be written as the solution set of a system of linear difference equations with constant coefficients. The resulting representation is known as the most powerful unfalsified model (MPUM) in behavioral systems theory. We address the case where the components of the given sequences take their values in a field, as well as the case where these values belong to a finite ring of the form ${{\mathbb{Z}}/m{\mathbb{Z}}}$ for an integer m > 1.     

On the Analysis of Cryptographic Assumptions in the Generic Ring Model

The generic ring model considers algorithms that operate on elements of an algebraic ring by performing only the ring operations and without exploiting properties of a given representation of ring elements. It is used to analyze the hardness of computational problems defined over rings. For instance, it is known that breaking RSA is equivalent to factoring in the generic ring model (Aggarwal and Maurer, Eurocrypt 2009). Do hardness results in the generic ring model support the conjecture that solving the considered problem is also hard in the standard model, where elements of ? _n are represented by integers modulo n? We prove in the generic ring model that computing the Jacobi symbol of an integer modulo n is equivalent to factoring. Since there are simple and efficient non-generic algorithms which compute the Jacobi symbol, this provides an example of a natural computational problem which is hard in the generic ring model, but easy to solve if elements of ? _n are given in their standard representation as integers. Thus, a proof in the generic ring model is unfortunately not a very strong indicator for the hardness of a computational problem in the standard model. Despite this negative result, generic hardness results still provide a lower complexity bound for a large class of algorithms, namely all algorithms solving a computational problem independent of a given representation of ring elements. From this point of view, results in the generic ring model are still interesting. Motivated by this fact, we also show that solving the quadratic residuosity problem generically is equivalent to factoring.     

High-speed signal processing using systolic arrays over finiterings

A modular architecture for very fast digital signal processing (DSP) elements are presented. The computation is performed over finite rings (or fields) and is able to emulate processing over the integer ring using residue number systems. The computations are restricted to closed operations (ring or field binary operators) with the ability to perform limited scaling operations. Computations naturally defined over finite mathematical systems are also easily implemented using this approach. The technique evolves from the decomposition of each closed calculation using the ring/field associativity property. Linear systolic arrays, formed with multiple elements, each of a single generic form, are used for all calculations. The pipeline cycle is determined from the generic cell and is predicted to be very fast by a critical path analysis. The cells are matched to the VLSI medium, and the resulting array structures are very dense. Examples of DSP applications are given to illustrate the technique, and example cell and array VLSI layouts are presented for a 3-μm CMOS process     

A semistate approach to feedback stabilization of neutral delay systems

In this paper we consider derivative feedback in a semistate framework for the problem of stabilizing the neutral root chains for a class of neutral delay-differential equations where the difference operator (orD-operator) is unstable. Recent work has shown that such systems cannot be stabilized by state feedback alone[3], [13], [16]. In addition, we consider the problem of using derivative feedback to eliminate all neutral root chains entirely, thus turning the closed loop system into a retarded delay system. By representing neutral delay-differential systems as semistate systems over a polynomial ring of delay operators, both of the above problems are shown to be reducible to the following question: Given matricesD,B over a commutative ringR, when does there exist a matrixM also overR such thatD+BM isR-unimodular? In the case of commensurable point delays our results are applications of some recent results on the simultaneous stabilization problem [19], and we give a constructive procedure for computing the required feedback law. In the case of noncommensurable delays we give a sufficient condition for the existence of suitable feedback for the above problems.     

Fast modulo-number Hadamard transformer for a sequency-division multiplexer

The implementation of a fast Hadamard transform that operates in the ring of p elements is described with particular applications in an adaptive sequency-division multiplexer. Maximum hardware efficiency is obtained if p is of the form 2r ? 1 for any r, and the data to be multiplexed are codcd in 1s-complement arithmetic. The advantage of transforming in a finite ring is that no extra bits are required to store the data as for real-number transforms.     

Determination of P-adic transform bases and lengths

The P-adic transform bases and lengths can be easily determined by the Hensel code weight sums defined over a finite ring Pr. The maximum transform length is found to be Pr?1(P?1) instead of(P?1), it has much wider choice and is longer than before in terms of transform size.     

Dual mode wideband band-pass filter with notched band for communication system

This paper presents a planar microstrip wideband dual mode Band-Pass Filter (BPF) from 2 GHz to 3.4 GHz with a notched band at 2.62 GHz. The dual mode band-pass filter consists of a ring resonator with two quarter-wavelength open-circuited stubs at ?? =90° and ?? =0°, respectively. A square perturbation stub has been put at the corner of the ring resonator to increase the narrow stopbands and improve the performance of selectivity. By using a parallel-coupled feed line, a narrow notched band is introduced at the required frequency and its Fractional BandWidth (FBW) is about 5%. The proposed filter has a narrow notched band and a wide pass-band with a sharp cutoff frequency characteristic, the attenuation rate for the sharp cutoff frequency responses is 297.17 dB/GHz (calculated from 1.959 GHz with ?34.43 dB to 2.065 GHz with ?2.93 dB) and 228.10 dB/GHz (calculated from 3.395 GHz with ?2.873 dB to 3.507 GHz with ?28.42 dB). This filter has the advantages of good insertion loss in both operating bands and two rejections of greater than 16 dB in the range of 1.59 GHz to 1.99 GHz and 3.49 GHz to 3.98 GHz. Having been presented in this article, the measurement results agree well with the simulation results, which validates our idea.     

Every discrete 2D autonomous system admits a finite union of parallel lines as a characteristic set

In this paper, we show that every discrete 2D autonomous system, that is described by a set of linear partial difference equations with constant real coefficients, admits a finite union of parallel lines as a characteristic set. In order to prove our claim, we first look at a special class of scalar discrete 2D systems and provide such characteristic sets for systems in this class. This special class has the property that systems in this class have their quotient rings to be finitely generated modules over a one-variable Laurent polynomial subring of the original two-variable Laurent polynomial ring in the shift operators. We show that such systems always admit a finite collection of horizontal lines for a characteristic set. We then extend this result to non-scalar discrete 2D autonomous systems. We achieve this in two steps: first, we show that every scalar discrete 2D system can be converted into a system in the above-mentioned class by a coordinate transformation on the independent variables set, \(\mathbb {Z}^2\). Using this we then show that characteristic sets for the original system can be found by applying the inverse coordinate transformation on characteristic sets of the transformed system. Since the transformed system, by virtue of being in the special class, admits a finite union of horizontal lines as a characteristic set, the original system is guaranteed to admit a characteristic set that is a coordinate transformation applied to a finite union of horizontal lines. The coordinate transformation maps this union of horizontal lines to a union of parallel, but possibly tilted, lines. In the next step, we generalize the scalar case to the general vector case: that is, systems with more than one dependent variables. The main motivation for studying characteristic sets that are unions of finitely many parallel lines is that, arguably, such sets can be called “thin” in \(\mathbb {Z}^2\) in comparison to the prevalent notions of convex cones and half-spaces as characteristic sets (see “Appendix 1”).     

A transform decoder for Reed-Solomon codes in multiple-user communication systems

Encoding and decoding algorithms for Reed-Solomon codes based on Fourier-like transforms on finite field and finite rings are discussed. Classes of codes are proposed for two different types of multiple-user communication systems: a multichannel communication system and a multiaccess communication system. For the first system, a fast decoding algorithm is developed that uses transforms on a finite ring which is isomorphic to a direct sum of Galois fields. For the second system, an efficient (in terms of information rate) coding scheme is proposed which utilizes a direct sum of Galois fields.     

Vibration control for active seat suspension systems via dynamic output feedback with limited frequency characteristic

This paper investigates the problem of H_∞ control for active seat suspension systems via dynamic output feedback control. A vertical vibration model of human body is introduced in order to make the modeling of seat suspension systems more precise. Meantime, different from the existing H_∞ control methods which conduct disturbance attenuation within the entire frequency domain, this paper addresses the problem of H_∞ control for active seat suspension systems in finite frequency domain to match the characteristics of the human body. By using the generalized Kalman-Yakubovich-Popov (KYP) lemma, the H_∞ norm from the disturbance to the controlled output is decreased over the chosen frequency band between which the human body is extremely sensitive to the vibration, to improve the ride comfort. Considering a practical situation of active seat suspension systems, a dynamic output feedback controller of order equal to the plant is designed, where an effective multiplier expansion is used to convert the controller design to a convex optimization problem. Compared with the entire frequency approach for active seat suspension systems, the finite frequency approach achieves better disturbance attenuation for the concerned frequency range, while the performance constraint is guaranteed in the controller design, which is verified by a practical example with certain and random road disturbances.     

The resonance properties of the near field in finite thin Veselago and Pendry lenses

The problem of excitation of a finite thin plate made from a metamaterial with the electrodynamic parameters ? _r ?? ?1, ?? _r ?? ?1 and ? _r ?? ?1, ?? _r = 1 by a point source is considered. Resonance phenomena in the near field of plates are found that are caused by the interaction of the formed surface waves. It is shown that the near field of the plate has the form of standing surface waves localized near wide faces of the plate, and the high Q factor of the observed resonances leads to the extremely strong dependence of the excited near-field amplitude on the electric and geometric parameters of the plates.     

一种新型基于MIM等离子体环形谐振器的可调谐高性能多信道波分解复用器的设计

设计并研究了基于金属-介质-金属等离子体环形谐振器的可调谐高性能多通道波分解复用器。通过环形腔的谐振理论分析,发现通过调节环形腔的半径和填充介质折射率可以很容易地控制波分复用器的信道波长,与有限元法模拟得到的结果吻合得很好。由等离子体波导和多个环形谐振器组成的多信道WDM结构增加了在电信波长的传输率,传输率高达80%,比最近文献中报道的结果高出两倍。所设计的多信道波分解复用器在高集成电路中有重要潜在应用。     

码长连续变化的QC-LDPC码的设计

该文基于有限多项式环的理论,提出了码长连续变化的准循环低密度奇偶校验(Quasi-Cyclic Low Density Parity Check, QC-LDPC)码的设计方法。当有限环基数大于某个门限值时,在此环内通过一定规则选择参数生成移位项,利用它们构造出的校验矩阵均可以达到较大的圈长(girth)值。在设计中,有限环基数为连续的整数,且基数与码长呈线性关系,因此能够在girth值不变的前提下实现码长的连续变化。该文分析并证明了该构造方法大大增加了可用的高性能QC-LDPC码数量,更好地服务于自适应链路系统。     

A novel proposal for all-optical decoder based on photonic crystals

In this paper, a new structure for all-optical 2-to-4 decoder is proposed which consists of six nonlinear photonic crystal ring resonators. The lattice constant of the main structure is a = 600 nm, and the refractive index and radii of rods are 3.1 and 0.2a, respectively. Simulation results have proved correct operation states of the decoder and numerical analysis is done in order to additional evaluation. The maximum and minimum power levels for logic 0 and 1 are \(0.1P_{\mathrm{in}}\) and \(0.37P_{\mathrm{in}}\) where \(P_{\mathrm{in}}\) is input power. The maximum cross talk and insertion loss are calculated about ?38 and ?20 dB, respectively. Since the operation speed of the decoder is more than 160 GHz, it will be appropriate candidate for being employed in ultrahigh-speed optical communication systems.     

Error performance of preamplified optical PPM systems with finite extinction ratios

In this paper, we present an analytical study of the error performance in optically preamplified, M-ary pulse position modulation, in free-space optical communication systems with finite extinction ratios. We derive a theoretical expression for the probability of bit error and compute it numerically for different symbol sizes and extinction ratios. We also provide the power penalty due to a finite extinction ratio for both coded and uncoded systems. The study shows that, in certain cases and for a given extinction ratio, lower symbol sizes may yield an error performance similar to that achieved by higher symbol sizes.     

Excitons and polaritons in AlGaAs semiconductor alloys

For Al_xGa_1?x As semiconductor alloys with x = 0.15 and 0.21 at temperatures T = 1.7?380 K, the band-edge absorption spectra are measured and the temperature dependence of the integrated absorption coefficient is obtained. The results are analyzed in the context of two mechanisms of the exciton-polariton energy transfer that can lead to the variation of the integrated absorption in systems with random excitonic potential at low temperatures. In one case, the temperature anomaly in the absorption results from the competition between the excitonic and electromagnetic mechanisms of the energy transfer in a quasi-homogeneous medium (a virtual crystal) with spatial dispersion. In the other case, the effect is related to the reemission of light by resonance localized excitons along finite chains of quantum wells in the absence of excitonic transfer. The observation of a characteristic temperature dependence of the integrated absorption supports the existence of exciton polaritons in the samples under study. It is found that integrated absorption in Al_0.15Ga_0.85As alloy saturates above the critical temperature T _c = 155 K. It is demonstrated that, in the temperature range from 1.7 to 60 K, the inhomogeneous broadening due to the fluctuating potential is responsible for the dominant contribution to the width of the excition line in the alloys investigated and considerably exceeds the homogeneous broadening caused by the interaction of excitons with phonons and charged impurities.     

0–30?V common mode range, 120?dB CMRR, and 10?nV/ \sqrt {\text{Hz}} noise floor current shunt monitor IC with an embedded ΣΔ modulated digital interface

Sensing and controlling current flow is a fundamental requirement for many electronic systems, including power management (DC?CDC converters and LDOs), battery chargers, electric vehicles, solenoid positioning, motor control, and power monitoring. Current shunt monitor (CSM) system enables current measurement across an external sense resistor (R _S ) in series to current flow. Proposed CSM system can sense a system (power supply) current from 1 to 500?mA across a typical board Cu-trace resistance of 1??? with less than 10???V input-referred offset, 150?nV/°C offset drift and 0.1% accuracy. Instead of using a costly zero-TC sense resistor (R _S ) that is used in typical CSM systems; proposed method uses existing Cu board trace for sensing. The sense amplifier uses chopper stabilization in the signal chain of the amplifier to suppress input-referred offset down to less than 10???V. Switching current-mode (SI) FIR filtering is used at the instrumentation amplifier output to filter out the chopping ripple at the harmonics of the chopping frequency. A frequency domain Sigma Delta (????FD) ADC enables a digital interface to processor applications. The CSM is fabricated on a 0.7???m CMOS process with three levels of metal with maximum Vds tolerance of 8?V, and operates across a common mode range of 0?C30?V achieving less than 10?nV/ $ \sqrt {\text{Hz}} $ of flicker noise at 100?Hz. By using a semi-digital SI FIR filter, residual chopper ripple is suppressed by more than 7.5?mV_pp from the base line of 8?mV_pp, which is equivalent to 25?dB suppression.     

Dynamic characteristics of double-barrier nanostructures with asymmetric barriers of finite height and widths in a strong ac electric field

The theory of the interaction of a monoenergetic flow of injected electrons with a strong high-frequency ac electric field in resonant-tunneling diode (RTD) structures with asymmetric barriers of finite height and width is generalized. In the quasi-classical approximation, electron wavefunctions and tunneling functions in the quantum well and barriers are found. Analytical expressions for polarization currents in RTDs are derived in both the general case and in a number of limiting cases. It is shown that the polarization currents and radiation power in RTDs with asymmetric barriers strongly depend on the ratio of the probabilities of electron tunneling through the emitter and collector barriers. In the quantum mode, when δ = ? ? ? _r = ?ω ? Γ (? is the energy of electrons injected in the RTD, ? is Planck’s constant, ω is the ac field frequency, ? _r and Γ are the energy and width of the resonance level, respectively), the active polarization current in a field of E ≈ 2.8?ω/ea (e is the electron charge and a is the quantum-well width) reaches a maximum equal in magnitude to 84% of the direct resonant current, if the probability of electron tunneling through the emitter barrier is much higher than that through the collector barrier. The radiation-generation power at frequencies of ω = 10¹²–10¹³ s^?1 can reach 10⁵–10⁶ W/cm² in this case.     

Constacyclic and cyclic codes over finite chain rings

The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.