Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1980"

A spatial processor model for object colour perception

Abstract: A comprehensive mathematical model to account for colour constancy is formulated. Since the visual system is able to measure true object colour in complex scenes under a broad range of spectral compositions, for the illumination; it is assumed that the visual system must implicitly estimate and illuminant. The basic hypothesis is that the estimate of the illuminant is made on the basis of spatial information from the entire visual field. This estimate is then used by the visual system to arrive at an estimate of the (object) reflectance of the various subfields in the complex visual scene. The estimates are made by matching the inputs to the system to linear combinations of fixed bases and standards in the colour space. The model provides a general unified mathematical framework for related psychophysical phenomenology.

Dissipative Dynamical Systems: Basic Input-Output and State Properties

Abstract: A complete account is given of the theory of so-called dissipative dynamical systems. The concept of dissipativeness is defined as a general input-output property which includes, as notable special cases, passivity and other properties related to finite-gain. The aim is to treat input-output and state properties side-by-side with emphasis on exploring connections between them. The key connection is that a dissipative system in general possesses a set of energy-like functions of the state. The properties of these functions are studied in some detail. It is demonstrated that this connection represents a direct generalization of the well-known Kalman-Yakubovich lemma to arbitrary dynamical systems. Applications to stability theory and passive system synthesis are briefly discussed for non-linear systems.

Model reduction using the stability-equation method and the Padé approximation method

Abstract: A combined method making use of the advantages of the stability-equation method and the Pade approximation method for reducing high order transfer functions of single-input/single-output systems and multivariable systems is presented. The reduction procedure is simple and computer-oriented. All the reduced models are guaranteed to be stable if the original system is stable. The proposed method is applied to the investigation of (1) the effect of model reduction on the limit-cycle of non-linear systems and (2) the effect of model reduction on Horowitz compensators. Detailed calculations are given and comparisons with results in the current literature are made.

Theory of broadband matching and the problem of compatible impedances

Abstract: It is shown that Youla's theory of broadband matching between a passive load and a resistive generator with a preassigned transducer power gain characteristic is completely equivalent to Wohlers' solution to the problem of compatible impedences, which transforms a given passive impedance by a lossless coupling network into another specified one.

On robust detection of discrete-time stochastic signals☆

Abstract: The problem of designing robust systems for the detection of stochastic signals in noise is considered for the large-sample-size, small-signal case. By applying two previously-established models for the detection of stochastic signals, known results for the robust detection of deterministic signals are extended on a limited basis to the stochastic- signal case. The proposed detectors are seen to be robust over a class of possible noise statistics, based on a Huber-Tukey mixture model, which contains noises characterized by heavy-tailed probability density functions. In addition, numerical results are presented which verify the robustness property of the proposed detectors over wider classes of noise mixtures.

Relevance of network theory to models of distributed/parallel processing☆

Abstract: This paper is concerned with the applicability of network theory to those aspects of distributed/parallel processing that can be modeled by marked graphs. First, several examples are given to illustrate that a wide variety of computation schemes can be modeled by marked graphs. Subsequently, the following topics are discussed: application of KVL to fault detection and isolation, KCL and Tellegen's Theorem applied to marked graphs, and the relationship between the maximum (minimum) storage requirement and the minimum (maximum) power.

Cutoff wavenumbers and the field of surface wave modes of an eccentric circular Goubau waveguide

Abstract: The cutoff wavenumbers knm and the field of surface wave modes of a circular cylindrical conductor eccentrically coated by a dielectric are determined analytically. The electromagnetic field is expressed in terms of circular cylindrical wave functions referred to both axes, in combination with related addition theorems. When the solutions are specialized to small eccentricities kd, where d is the distance between the two axes, exact closed-form expressions are obtained for the coefficients gnm in the resulting relation knm(d)=knm(0)[1+gnm(knmd)2+...] for the cutoff wavenumbers of the waveguide. Similar expressions are obtained for the field. Numerical results for all types of modes are given. For certain values of the parameters, it is possible to enhance the operating bandwidth of the basic hybrid mode HE11 over the conventional concentric guide.

An active-rc biquadratic section with reduced sensitivity to operational amplifier imperfections

Abstract: A new active RC biquadratic section using three operational amplifiers (op. amps) and capable of realizing high Q at high frequencies is presented. The circuit has low-sensitivity to variations in both the passive components and the op. amp gain-bandwidth products (GB). Compared to some existing circuits which require well-matched op. amps to achieve low sensitivity to GB, the proposed circuit has the important advantage of being insensitive to GB variations even if the op. amps are non-identical. The influence of the finite open loop d.c. gain and finite GB of the op. amps on the proposed design is examined. The new realization is then compared to those available in the literature, such as the circuits due to Kerwin–Huelsman–Newcomb, Akerberg–Mossberg, Mikhael–Bhattacharyya, Tarmy–Ghausi, and Wilson–Bedri–Bowron. Finally, some experimental results are provided to verify the theory.

A Detection Scheme for Dependent Noise Processes

Abstract: In this paper the problem of memoryless discrete time detection of a constant signal in additive φ-mixing noise is considered. The fidelity criterion is taken to be the asymptotic relative efficiency. The optimal detector nonlinearity is approximated by a polynomial, and the statistical knowledge required for the design of the detector is the family of joint moments of the noise, resulting in a very simple design procedure for the detector. It is shown that the performance of this detector can be made arbitrarily close to that of the optimal memoryless detector for a large class of noises.

The Thermal Sensitivity of Michaelis-Menten Kinetics as a Function of Substrate Concentration

Abstract: Analysis of the thermal sensitivity of life processes governed by Michaelis-Menten kinetics shows that: (1) a one-parameter family of either isotherms or isoconcentrates is required to describe the thermal sensitivity of such processes; (2) rate maxima cannot exist unless a single parameter condition is satisfied and substrate concentration falls within a well-defined range; (3) optimum temparature increases asthe logarithm of substrate concentration and semi-log plots of optimum temperature (linear scale) versus substrate concentration (logarithmic scale) yield straight lines; (4) the maximum rate corresponding to the optimum temparature increases as substrate concentration raised to a power of value less than unity and log-log plots of maximum rate versus substrate concentration produce straight lines with less-than-unity slopes; and (5) the progression of optimum temperature and maximum rate with substrate concentration is parallel to the infinite-concentration isoconcentrate in semi-log plots, with rate plotted on the logarithmic scale and temperature on the linear scale.

Scattering from Spheroidal Composite Objects

Abstract: The exterior scattering problem of electromagnetic waves from spheroidal objects or particles is considered. The particles are assumed to be composed of electrically dissimilar materials. This necessitates the modelling of the particle, for the exterior scattering problem, in terms of an inhomogeneous surface impedance. In this manner, the Leontovich boundary condition and the Moments method are invoked, to provide the solution to the scattering problem.

Transient heat conduction in an anisotropic medium in cylindrical coordinates

Abstract: Three dimensional, time dependent heat conduction for an anisotropic medium of a triclinic system is solved for an infinitely long hollow or solid cylinder of finite radius with a restriction e 23 = e 12 e 13 . Several special cases are obtained from the present solution.

On the uniqueness of the minimal solution to the matrix polynomial equation A(λ)X(λ)+Y(λ)B(λ)=C(λ)

Abstract: The uniqueness of the minimal solution of the matrix equation A(λ)X(λ)+Y(λ)B(λ)=C(λ) is discussed in this paper. It is proved that Barnett's condition for uniqueness can be obtained when only A(λ) or B(λ) (not necessarily both) is regular. Furthermore, it is shown that if such a minimal solution exists, it is not unique if and only if both matrices are nonregular.

Experimental study of the critical speed response, of a jeffcott rotor with acceleration

Abstract: A small, lightly damped rotor (ζ=0.0088) was experimentally tested for a variety of acceleration and deceleration rates. In each case, the amplitude response was plotted as a function of operating speed, with the acceleration rate considered. In each case the results are compared with theoretical predictions. The results agree within 6% at the peak response. The results of the analysis indicate that for high acceleration rates the critical amplitude response may be reduced by a factor of four or more. The frequency of the effective critical speed may be shifted by up to 20%. Furthermore, a beating frequency was observed in the amplitude data after the rotor had passed through the critical speed. This phenomenon is shown to be the vector sum of a synchronous component of amplitude and a nonsynchronous transient component (at the critical speed). The transient nonsynchronous component is shown explicitly via electronic band-pass filtering, as is the forced response component. Finally, spectral analyses were performed over a range of operating speeds, yielding waterfall diagrams and further verification of the existence of the two components.

The graph-theoretic field model— II. application of multi-terminal representations to field problems

Abstract: This paper is a sequel to a paper entitled “The Graph-Theoretic Field Model—I: Modelling and Formulations” (1). Herein, the Theory of Multi-Terminal Representations is applied to the Graph-Theoretic Field Model to provide mathematical models of finite elements. The element models are obtained solely from the algebraic building blocks of the Graph-Theoretic Field Model, without recourse to any functional mathematics. The theory of Multi-Terminal Representations is developed for both linear and non-linear problems. Examples of the application of the theory to one- and two-dimensional field problems are presented from heat conduction and electrostatics.

Simplification of large linear systems using a two-step iterative method

Abstract: A simple iterative technique, which is free of certain shortcomings of the previous methods, is proposed for the approximation of large linear systems by a lower- order model. Here, the measure of the goodness of the approximate model is taken to be the value of the integral-square error between the step responses of the exact and the simplified systems. The proposed technique consists of a two-step iterative scheme. In the first step, the optimum residues are obtained by the minimization of the objective function, while the poles (or eigenvalues) are kept constant. In the second step, the poles are optimized while the residues remain fixed. This procedure is continued cyclically until the objective function is satisfactorily minimized. The necessary and sufficient conditions for existence of an optimum are satisfied in each step. The residues, poles and objective functions converge monotonically. The resulting reduced-order model obtained by this method is stable if the original system is stable. The method can also be applied to systems with repeated poles and to multivariable systems. The results are superior to those obtained previously in the steady-state, the point-by-point transient response, and the value of the integral-square error. Illustrative examples are presented.

Derivation of the Brayton–Moser equations from a topological mixed potential function

Abstract: A topological mixed potential function, P*T, is defined and shown to be an exact differential. From P*T, the Brayton-Moser equations are obtained from topological relationships of the network and the constitutive relationships of the elements. A relationship between P*T and Brayton-Moser's mixed potential function, Q, is developed.

Stabilized generation of precise triangular waves, square waves and trapezoidal waves in three phases

Abstract: A new three-dimensional compact oscillator model for generating three phases of triangular waves and square waves (and also trapezoidal waves) is developed by considering carefully a recently suggested model for the precise quadrature generation of similar waves in two phases. The properties of the solution of the new model equations are investigated and they suggest that the oscillator should possess applications for the design of relatively simple electronic three phase triangular and square wave generators. “Software” applications of the model and its employment for power systems simulations are also discussed briefly.

An Algorithm for Incorporating Subsystem Models into Overall Dynamic System Models

Abstract: Bond graphs are used to construct finite mode representations of inherently distributed systems. These systems are, perhaps, only part of an overall dynamic system. The “causal” information provided by the bond graph permits the derivation of an automatable algorithm which produces the state equations as well as all output variables associated with the finite modes. The procedure requires only the a priori knowledge of modal masses, frequencies, and associated mode shapes for general boundary conditions of the distributed parts of the system. Thus, the algorithm is applicable to any multidimensional distributed system which is representable by normal modes.

Design of minimum sensitivity multiple loop feedback bandpass active filters

Abstract: A method is described for determining multiple loop feedback topologies which yield minimum sensitivities for symmetrical, all-pole bandpass filters. The procedure begins with a follow-the-leader feedback (FLF) topology and additional feedback loops are constructed until minimum sensitivity is achieved. Filters comprised of identical second-order sections and non-identical sections, respectively, are considered.

On metrics matched to the discrete memoryless channel

Abstract: A sequence of metrics {D N } is said to be additive and matched to a discrete memoryless channel (DMC) if D N is the sum on its coordinates of N single letter metrics and if the maximum likelihood decoder for sequences of length N is a minimum D N -distance decoder. Necessary and sufficient conditions on the transition probabilities of a DMC for the existence of a sequence of additive metrics matched to it are given. In the case of the binary channel these are shown to be equivalent to the channel being symmetric. Explicit transition probabilities are given for a large class of ternary DMCs with an associated sequence of additive matched metrics. The problem solved here may be considered a generalization of the problem of finding the DMCs matched to the Lee metric solved by Chiang and Wolf in 1971 ( 2 ).

Unified theory of broadband matching

Abstract: The paper presents a unified summary of recent progress on mathematical theory of broadband matching. It is shown that the characterization of the normalized scattering matrix, the problem of compatible impedances and the matching of an arbitrary load to a frequency-dependent source to give a preassigned transducer power-gain characteristic can all be stated in terms of the more convenient basic coefficient constraints. Thus, the three problems are in fact three facets on the existence of a complex normalized scattering matrix.

The Analytic Representation of Band-Pass Signals

Abstract: The analytic representation of band-pass signals, which is extremely useful in information transmission and radar, is usually obtained by first introducing the Hilbert transform of a signal. We consider this procedure artificial, and propose here to follow the opposite path, which leads, in a natural way, to a motivated definition of the Hilbert transform. The key to this procedure is to show how, as a simple application of the Fourier integral, every band-pass signal can be expressed as the real part of a low frequency signal which modulates an exponential. Such a representation, called the analytic signal, is then used to define the Hilbert transform in a natural manner. Finally, we show that the term analytic signal is motivated by the fact that this signal is the restriction to the real axis of a function defined and analytic (holomorphic) in the upper half of the complex plane.

Distributed-parameter optimal control via mathematical programming

Abstract: In this paper a variety of optimal control (OC) problems for distributed- parameter (DP) systems are approached using mathematical programming (MP). First, the principal DP models in current use are given, a variety of DP objective functions is provided, and the OC problems based on them are formulated. Second, these models and objective functions are converted in algebraic form, as required by MP, and the solution procedure of the OC problems via MP is outlined. Third, a representative set of nonlinear programming results applied to DP systems is presented, and finally, a numvber of application examples is given.

A Quantitative Stability Analysis of the Solutions to the Carson-Cambi Equation

Abstract: A quantitative stability analysis of the Carson-Cambi equation [(1 + e cos t )(d 2 y /d t 2 ) + py = 0] is carried through, using a new, effective approach. The results are compared with a recent perturbation analysis, and show that this should not be used for e0.4. In the present analysis we go up to e = 0.8, and, in fact, with less effort than the perturbation analysis involves. Detailed stability diagrams are presented.

Properties of the maximal correlation function

Abstract: Sarmanov introduces the idea of maximal correlation function and applies it to his investigation of stationary Markov processes ( 1 , 2 , 3 ). We demonstrate some additional properties of the maximal correlation function as a measure of the dependence structure of stationary processes and present some applications of the maximal correlation function in generalizing applications of the usual correlation function to, for example, equivalent rectangular bandwidth and quadratic mean ergodicity.

Electrodynamics of solid-rotor induction machines

Abstract: In this paper a simplified model of the solid-rotor induction machine is discussed. Analysis is provided on the basis of Maxwell's equations yielding a dimensionless thrust-slip characteristic which permits rapid evaluation of various machine parameters in its performance. The salient feature of this kind of induction device—flat thrust-slip response—is borne out by the obtained curves.

Complementary formulations in vibrations: bond graph structures and modal transformations

Abstract: Lumped parameter, undamped vibratory system models are studied starting from a vector bond graph representation which yields a symmetric set of equations of motion in terms of momenta and displacements. Four additional formulations are obtained depending upon the choices of displacement or impulse-momentum degrees of freedom including the classical formulation in terms of mass displacements. Differences in terms of forcing and response variables are found among the alternative formulations and differences in system order are explained. A new form of normal mode equations is developed using first order symmetric variables and a bond graph representation is given. Advantages in the use of the new model analysis for subsystem coupling are discussed.