Gaussian radial basis functions and inner product spaces

An approximation result is given concerning Gaussian radial basis functions in a general inner product space. Applications are described concerning the classification of the elements of disjoint sets of signals, and also the approximation of continuous real functions defined on all of ⁿ using radial basis function (RBF) networks. More specifically, it is shown that an important large class of classification problems involving signals can be solved using a structure consisting of only a generalized RBF network followed by a quantizer. It is also shown that Gaussian radial basis functions defined on ⁿ can uniformly approximate arbitrarily well over all of ⁿ any continuous real functionalf on ⁿ that meets the condition that |f(x)|0 as x.     

On the design of feedback controllers to achieve prescribed initial value constraints

The problem of designing a stabilizing compensator for a control system to achieve prescribed initial value constraints ⁽ⁱ⁾(0⁺)=y_i is considered. Indeed, modulo certain technical conditions, such a compensator exists if and only if y_i=0;i= 0,1,...,rp +rt –2; whererp is the relative degree of the plant andrt is the relative degree of the system input. This theorem is derived and a complete parameterization of the set of compensators that achieve the prescribed design constraints is formulated.This research was supported in part by NSF Grant No. 921106.     

Symmetry relations in multidimensional Fourier transform pairs

A relation between the types of symmetries that exist in signal and Fourier transform domain representations is derived for continuous as well as discrete domain signals. The symmetry is expressed by a set of parameters, and the relations derived in this paper will help to find the parameters of a symmetry in the signal or transform domain resulting from a given symmetry in the transform or signal domain respectively. A duality among the relations governing the conversion of the parameters of symmetry in the two domains is also brought to light. The application of the relations is illustrated by a number of two-dimensional examples.Notation R the set of real numbers - R ^m R × R × ... × R m-dimensional real vector space - continuous domain real vector - L {¦ – _i , i = 1,2,..., m} - m-dimensional frequency vector - W { – _i ,i=1,2,..., m} - m-dimensional normalized frequency vector - _P {¦ – _i , i=1,2,...,m} - g(ol) g (₁,₂,..., _m ) continuous domain signal - () ( _{1 2},..., _m )=G (j ₁,j ₂,..., j _m ) Fourier transform ofg (ol) - (A,b,,,) parameters ofT- symmetry - N the set of integers - N ^m N × N × ... × N m-dimensional integer vector spacem-dimensional lattice - h(n) h (n ₁,.,n _m ) discrete domain signal - H() Fourier transform ofh (n) - v ₁,v ₂,..., v_m m sample-direction and interval vectors - V (v ₁ v ₂ ...v _m ) sampling basis matrix - [x]^* complex conjugate ofx - detA determinant ofA - X {x¦ – x _i , i=1,2,..., m} - A ^–t [A ^–1] ^t ,t stands for transpose This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-7739 to M. N. S. Swamy and in part by Tennessee Technological University under its Faculty Research support program to P. K. Rajan.     

Quality Determination for Gate Delay Fault Tests Considering Three-State Elements

Most industrial digital circuits contain three-state elements besides pure logic gates. This paper presents a gate delay fault simulator for combinational circuits that can handle three-state elements like bus drivers, transmission gates and pulled busses. The well known delay faults--slow-to-rise and slow-to-fall--are considered as well as delayed transitions from isolating signal state high impedance to binary states 0 and 1 and vice versa. The presented parallel delay fault simulator distinguishes between non-robust, robust and hazard free tests and determines the quality of a test. Experimental results for ISCAS85/89 benchmark circuits are presented as well as results for industrial circuits containing three-state elements.     

Geometric properties of nonlinear networks containing capacitor-only cutsets and/or inductor-only loops. Part I: Conservation laws

This paper is the first in a two part sequence which studies nonlinear networks, containing capacitor-only cutsets and/or inductor-only loops from the geometric coordinate-free point of view of differentiable manifolds. Given such a nonlinear networkN, with °₀ equal to the sum of the number of independent capacitor-only cutsets and the number of independent inductor-only loops, we establish the following: (i) circuit theoretic sufficient conditions to guarantee that the set ⁰, of equilibrium points is a ₀-dimensional submanifold of the state space ofN; (ii) circuit theoretic sufficient conditions for the condition thatN has ₀ independent conservation laws and hence that through each point of the state space ofN, there passes a codimension ₀ invariant submanifold ^* of the network dynamics; (iii) circuit theoretic sufficient conditions to guarantee that the manifolds ^* and ⁰ intersect transversely.This work was supported by the Natural Sciences and Engineering Research Council of Canada, under Grant Number A7113, and by scholarships from the Natural Sciences and Engineering Research Council of Canada and the Ontario Provincial Government.     

β-bit serial/parallel multipliers

A generalized -bit least-significant-digit (LSD) first, serial/parallel multiplier architecture is presented with 1n wheren is the operand size. The multiplier processes both the serial input operand and the double precision product -bits per clock cycle in an LSD first, synchronous fashion. The complete two's complement double precision product requires 2n/ clock cycles. This generalized architecture creates a continuum of multipliers between traditional bit-serial/parallel multipliers (=1) and fully-parallel multipliers (=n). -bit serial/parallel multipliers allow anoptimized integrated circuit arithmetic to be designed based on a particular application's area, power, throughput, latency, and numerical precision constraints.This project was pratically funded by the UCSD-NSF I/UCR Center on Ultra-High Speed Intergrated Circuits and Systems.     

Distance of a complex coefficient stable polynomial from the boundary of the stability set

In this paper, the distance in the 1 2p norm from a complex coefficient polynomial to the border of its Hurwitz region is analyzed. Simplified expressions for 2p=1, 2, are also obtained.This work was supported in part by Comisión Investigaciones Cientificas de la Provincia de Buenos Aires (CIC) and Comisión Nacional de Investigaciones Cientificas y Técnicas (CONICET).     

Efficient linear-phase FIR, maximally flat error approximations for the amplitude response |1/ω r |,r,r=1, 2, 3,..., and a versatile realization

In this paper, designs of linear-phase finite impulse response (FIR) filters approximating the ideal frequency responseH (,r) |1/ ^r r=1, 2, 3,..., by using maximally flat error criteria have been proposed. Exact weights required for the realizations have been derived and are shown to be independent of the filter orderN. The suggested designs are particularly suitable for operation in the midband frequency range of 0.10–0.90 radians.     

Systematic Width-and-Length Dependent CMOS Transistor Mismatch Characterization and Simulation

This paper presents a methodology for characterizing the random component of transistor mismatch in CMOS technologies. The methodology is based on the design of a special purpose chip which allows automatic characterization of arrays of NMOS and PMOS transistors of different sizes. Up to 30 different transistor sizes were implemented in the same chip, with varying transistors width W and length L. A simple strong inversion large signal transistor model is considered, and a new five parameters MOS mismatch model is introduced. The current mismatch between two identical transistors is characterized by the mismatch in their respective current gain factors /, V _TO threshold voltages , bulk threshold parameters , and two components for the mobility degradation parameter mismatch ₀ and _e. These two components modulate the mismatch contribution differently, depending on whether the transistors are biased in ohmic or in saturation region. Using this five parameter mismatch model, an extraordinary fit between experimental and computed mismatch is obtained, including minimum length (1 m) transistors for both ohmic and saturation regions. Standard deviations for these five parameters are obtained as well as their respective correlation coefficients, and are fitted to two dimensional surfaces f(W, L) so that their values can be predicted as a function of transistor sizes. These functions are used in an electrical circuit simulator (Hspice) to predict transistor mismatch. Measured and simulated data are in excellent agreement.     

Predictive Caching Strategy for On-Demand Routing Protocols in Wireless Ad Hoc Networks

Route caching strategy is important in on-demand routing protocols in wireless ad hoc networks. While high routing overhead usually has a significant performance impact in low bandwidth wireless networks, a good route caching strategy can reduce routing overheads by making use of the available route information more efficiently. In this paper, we first study the effects of two cache schemes, link cache and path cache, on the performance of on-demand routing protocols through simulations based on the Dynamic Source Routing (DSR) protocol. Since the path cache DSR has been extensively studied, we focus in this paper on the link cache DSR in combination with timer-based stale link expiry mechanisms. The effects of different link lifetime values on the performance of routing protocol in terms of routing overhead, packet delivery ratio and packet latency are investigated. A caching strategy incorporating adaptive link timeout is then proposed, which aims at tracking the optimal link lifetime under various node mobility levels by adaptively adjusting the link lifetime based on the real link lifetime statistics. The performance of the proposed strategy is then compared with the conventional path cache DSR. The results show that without a timeout mechanism, a link cache scheme may suffer severe performance degradation due to the use of broken routes, while the proposed adaptive link cache strategy achieves significantly improved performance by reducing the routing overhead when the network traffic load is high.     

A VLSI decoder for a new type of constellations adapted to the Rayleigh Fading Channel

Diversity is the key solution to obtain efficient channel coding in wireless communications, where the signal is subject to fading (Rayleigh Fading Channel). For high spectral efficiency, the best solutions used nowadays are based on QAM constellations of 1-order diversity, associated with a binary code or a trellis coded modulation to increase the overall diversity. It has been shown that a new class of d-dimensional non-QAM constellations, named -constellations, can bring a d-order diversity without the addition of redundancy. Combined with classical coding techniques, -constellations are very efficient. However, the decoding algorithm is far more complicated for -constellations than for QAM-constellations. A sub-optimal algorithm that allows the decoding of -constellations is proposed. An example of an application for a 4 bits/Hz/s spectral efficiency with a 4-D -constellation is given. The VLSI architecture of the decoder is described. The implementation leads to 72 K gates, a binary rate of 32 Mbits/s and a BER of 10^-3 for a SNR of 14 dB.     

A holographic transform domain image watermarking method

A transform domain image tagging orwatermarking method that survives image cropping (and, hence, is holographic) was proposed at Bell Labs in September 1994. This report analyzed in detail the various properties of this method and introduces an optimal procedure for watermark recovery.     

The discrete Einstein relation

In this paper the connection between massM, resistance and commute time for random walks on graphs is further explored, and the relation=2M · is proved. An extension of the result is made to multigraphs, which are an extension of the graph concept where a black box is treated like an edge.     

Consistency management in Deno

We describe a new replicatedobject protocol designed for use in mobile and weaklyconnected environments. The protocol differs from previous protocols in combining epidemic information propagation with voting, and in using fixed perobject currencies for voting. The advantage of epidemic protocols is that data movement only requires pairwise communication. Hence, there is no need for a majority quorum to be available and simultaneously connected at any single time. The protocols increase availability by using voting, rather than primarycopy or primarycommit schemes. Finally, the use of perobject currencies allows voting to take place in an entirely decentralized fashion, without any server having complete knowledge of group membership. We show that currency allocation can be used to implement diverse policies. For example, uniform currency distributions emulate traditional voting schemes, while allocating all currency to a single server emulates a primarycopy scheme. We present simulation results showing both schemes, as well as the performance advantages of using currency proxies to temporarily reallocate currency during planned disconnections. Furthermore, we discuss an initial design of the underlying replicatedobject system and present a basic API.     

Signal Processing for Large Bandwidth and Long Duration Waveform SAR

We first show that for some kinds of signals a bandwidth and time duration reduction technique can be used to simulate waveform distortions caused by moving targets, that is, it is correct to measure the waveform distortions at very large TB with relatively small by reducing TB and increasing while keeping TB unchanged, where T is the duration of the transmitted signal, B is the bandwidth and is the relative speed of targets. We then study the waveform distortions in SAR signals caused by moving antenna. Based on the bandwidth and time duration reduction technique, a lot of time and memory are saved in simulations. We then confirm by simulations that waveform distortions do pose problems when processing very large bandwidth and long duration SAR data using conventional SAR processing methods. Finally we propose the concepts of wideband and narrowband processing of SAR data. Models are set up for wideband and narrowband SAR data processing, and new methods are presented for reconstructing targets using the proposed models. Simulations show that the methods can improve the quality of the simulated SAR images.     

Perspectives on Analytical Modeling of Small Geometry MOSFETs in SPICE for Low Voltage/Low Power CMOS Circuit Design

The present state of the art in analytical MOSFET modeling for SPICE circuit simulation is reviewed, with emphasis on the circuit design usage of these models. It is noted that the model formulation represents an upper limit of what is possible from any type of model, but that good parameter extraction is required to most closely approach that limit. The individual model types presently in common use are examined, with discussion of the behavior of each model, its strengths and weaknesses, its applicability to certain types of circuits, and criteria that a circuit design consumer can employ to judge a model before using it for circuit design. Some related issues, such as node charge and gate capacitance modeling, charge conservation, and statistical simulation of process variations, are also evaluated. Finally, new trends, directions, and requirements of MOSFET modeling for circuit simulation are considered.     

On the distribution of characteristics in bijective mappings

Differential cryptanalysis is a method of attacking iterated mappings based on differences known as characteristics. The probability of a given characteristic is derived from the XOR tables associated with the iterated mapping. If is a mapping : Z ₂ ^m , then for each , X, Y Z ₂ ^m the XOR table for gives the number of input pairs of difference X=X+X for which gp(X)+(X)=Y.The complexity of a differential attack depends upon two properties of the XOR tables: the density of zero entries in the table, and the size of the largest entry in the table. In this paper we present the first results on the expected values of these properties for a general class of mappings . We prove that if : Z ₂ ^m Z ₂ ^m is a bijective mapping, then the expected size of the largest entry in the XOR table for is bounded by 2m, while the fraction of the XOR table that is zero approaches e ^–1/2=0.60653. We are then able to demonstrate that there are easily constructed classes of iterated mappings for which the probability of a differential-like attack succeeding is very small.The author is presently employed by the Distributed System Technology Center, Brisbane, Australia.     

Time‐varying modeling of a nonstationary signal

In this paper, a method for modeling a nonstationary signal using timevarying parameters by considering that the signal is generated by a linear, timevarying (LTV) system with a stationary white noise input is presented. This method is based on the Wold–Cramer (WC) representation of a nonstationary signal. Because the relationship between the generalized transfer function of an LTV system and the timevarying coefficients of the difference equation of a discretetime system is not addressed so far in the literature, therefore, in this paper a solution to this problem is proposed. A simple relationship between the system generalized transfer function and the timevarying parameters of the system is derived, then an MLS algorithm is developed to solve for the system timevarying parameters. Computer simulation illustrating the effectiveness of our algorithm is presented.     

Some properties of order-Statistics filters

LetX ₁,X ₂,... be a stationary sequence of random variables with Pr{X _t, x}=F(x),t=1, 2,... Also let _i ^n,(t) ,i=1,...,n, denote the ith order statistic (OS) in the moving sample (X _t–N ,...,X _t,...,X _t+N) of odd sizen=2N+1. ThenY _t=a _i X _i ^n(t) with a _i=1 is an order-statistics filter. In practicea _i0,i=1,...,n. Fort>N, the sequence {Y _t} is also stationary. IfX ₁ X ₂, ... are independent, the autocorrelation function (r)=corr(Y _t,Y _t+r) is zero forr >n – 1 and forr n – 1 can be evaluated directly in terms of the means, variances, and covariances of the OS in random samples of sizen +r fromF(x).In special cases several authors have observed that the spectral density functionf() of {Y _t} is initially decreasing for > 0. This result is made more precise and shown to hold generally under white noise. The effect of outliers (impulses) is also discussed.This research was supported by the U.S. Army Research Office.