A 50-MHz CMOS amplifier channel for a laser radar

An integrated CMOS amplifier channel consisting of a transimpedance preamplifier, postamplifiers, and gain control circuitry has been designed for the receiver of a pulsed time-of-flight laser radar. The measurement results, a total transimpedance ofZ _t 250 k with a bandwidth ofBW 65 MHz and an input-referred noise current ofi _ni 7 pA/Hz, show that a range measurement resolution of centimeter/decimeter class could be achieved by detecting the edge of the received laser pulse.     

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.     

On the structure of the privacy hierarchy

An N argument function f(x ₁,...,x _N ) is called t-private if a protocol for computing f exists so that no coalition of at most t parties can infer any additional information from the execution, other than the value of the function. The motivation of this work is to understand what levels of privacy are attainable. So far, only two levels of privacy are known for N argument functions which are defined over finite domains: functions that are N-private and functions that are (N – 1)/2-private but not N/2-private.In this work we show that the privacy hierarchy for N-argument functions which are defined over finite domains, has exactly (N + 1)/2 levels. We prove this by constructing, for any N/2 t N – 2, an N-argument function which is t-private but not (t + 1)-private.This research was supported by US-Israel Binational Science Foundation Grant 88-00282.     

Conservative Input–State–Output Systems with Evolution on a Multidimensional Integer Lattice

A fundamental object of study in both operator theory and system theory is a discrete-time conservative system (variously also referred to as a unitary system or unitary colligation). In this paper we introduce three equivalent multidimensional analogues of a unitary system where the time axis , d>1, is multidimensional. These multidimensional formalisms are associated with the names of Roesser, Fornasini and Marchesini, and Kalyuzhniy–Verbovetzky. We indicate explicitly how these three formalisms generate the same behaviors. In addition, we show how the initial-value problem (including the possibility of initial conditions at infinity) can be solved for such systems with respect to an arbitrary shift-invariant sublattice as the analogue of the positive-time axis. Some of our results are new even for the d=1 case.First online version published in May 2005*The authors were supported in part by a grant from the US-Israel Binational Science Foundation.     

Order selection statistical test for nonstationary AR models

A new statistical test for selecting the order of a nonstationary AR modelyk is presented based on the predictive least-squares principle. This test is of the same order as the accumulated cost function _n = _k=1 ⁿ ( _k ^* – _k )²;i.e., ^* wherey _k ^* is the predictive least-square estimate. It is constructed to show how many times the integrated AR processy _k is differenced in order to obtain a stationary AR process given that the exact order of the process is unknown.     

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.     

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).     

Quantitative analysis for linear hybrid cellular automata and LFSR as built-in self-test generators for sequential faults

This paper presents a combinatorial method of evaluating the effectiveness of linear hybrid cellular automata (LHCA) and linear feedback shift registers (LFSR) as generators for stimulating faults requiring a pair of vectors. We provide a theoretical analysis and empirical comparisons to see why the LHCA are better than the LFSRs as generators for sequential-type faults in a built-in self-test environment. Based on the concept of a partner set, the method derives the number of distinctk-cell substate vectors which have 2^2k , 1k[n/2], transition capability for ann-cell LHCA and ann-cell LFSR with maximum length cycles. Simulation studies of the ISCAS85 benchmark circuits provide evidence of the effectiveness of the theoretrical metric.This work was supported in part by Reserach Grants No. 5711 and No. 39409 and a Strategic Grant from the Natural Sciences and Engineering Research Council of Canada and by an equipments loan from the Canadian Microelectronics Corporation.A preliminary version of this paper is partially presented at theIEEE ISCAS'94, May 1994.     

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.     

Construction of Time-Relaxed c-Broadcast Networks

C-broadcasting is an information dissemination task where a message, originated at any node in a network, is transmitted to all other nodes with the restriction that each node having the message can transmit it to almost c neighbors simultaneously. If the transmission time of the message is set to be one time unit, a minimal c-broadcast network (c-MBN) is a communication network in which c-broadcasting from any node can be accomplished in log _c+1 n time units, where n is the number of nodes and log _c+1 n is the fastest possible broadcast time. If networks are sparse, additional time units may be required to perform c-broadcasting. A time-relaxed c-broadcast network, denoted as (t,c)-RBN, is a network where c-broadcasting from any node can be completed in log _c+1 n+t time units. In this paper, a network compounding algorithm is proposed to construct large sparse (t,c)-RBNs by linking multiple copies of a time-relaxed network of small size using the structure of another time-relaxed network. Computational results are presented to show the effectiveness of the proposed algorithm.     

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.     

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.     

Using a WLFSR to Embed Test Pattern Pairs in Minimum Time

We propose a methodology for reducing the number of test cycles needed by a Weighted LFSR (WLFSR) to reproduce a 2P × W test matrix T of P pattern pairs. The methodology introduces a very small number of extra cells into the WLFSR and uses appropriate combinational mapping logic in order to make the time be equal to that required by a (W + )-bit WLFSR to generate vectors containing the W bits of the first pattern for each pair plus the extra bits. We present an algorithm that makes the value of be less than or equal to log₂, where is the size of the maximum subset of pairs in T with identical first patterns. This is a significant improvement over the time E _P,W · P required by a trivial approach that uses a WLFSR with W cells to generate the first patterns of the pairs and a P × W ROM to store the second patterns of the pairs. Experimental results on the application of the methodology to the embedding of test matrices for path delay faults are particularly encouraging, even for very large numbers of test pattern pairs that are necessary for provably high fault coverage.     

Relations between thek-dimensional unconstrained and linear phase FIR Wiener filters

In this note, we show that thek-dimensional linear phase FIR Wiener filter can be obtained from the unconstrained filter with a simple reverse and add operation. The relation between the linear phase and unconstrained phase filters is obtained also in the case of a multichannelk-dimensional system. In this case, the properties of the autocorrelation matrix do not allow the simplifications noted for the single channel case.     

Input-output systems whose transmission operators furnish nearly best approximations to a given map

Let {S(A):A A}, whereA is a subset of an infinite-dimensional normed linear spaceL, be a class of general nonlinear input-output systems that are governed by operator equations relating the input, state, and output, all of which are in extended spaces. IfQ is a given operator from a specified set ¯D _i, of inputs into the space of outputs ¯H ₀, the problem we consider is to find, for a given >0, a parameterA A such that the transmission operatorR(A ) ofS(A ) furnishes a nearly best (or -best) approximation toQ from allR(A),A A. Here the distance betweenQ andR(A) is defined as the supremum of distances betweenQz andR(A)z taken over allz ¯D _i. In Theorems 2 through 5 we show that ifS(A) is normal (Definition 2),A satisfies some mild requirement andL contains a fundamental sequence, then establishingA A reduces to minimizing a certain continuous functional on a compact subset ofR ⁿ, and thus can be carried out by conventional methods. The applications of results are illustrated by the example of a model-matching problem for a nonlinear system, and of optimal tracking.     

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.     

Systems which possessg- andh- Representations

Examples are given concerning the range of applicability of recent representation results that provide a means of studying the input-output properties of nonlinear systems in terms of the familiar impulse-response concept, and which extend the concept of integral transformation to nonlinear maps. We show that such representations, which we call g- and h-representations, exist for important classes of systems governed by nonlinear integral equations. In particular, it is proved that a large class of maps that have Volterra series representations also have these representations.     

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.     

Estimation of Energy Aliasing Error for Nonbandlimited Signals

In this paper, we investigate the problem of approximating a given (not necessarily bandlimited) signal, x(t), by a (bandlimited) interpolation or sampling series of the form: