Exact Realization Research Articles

Microscopic approach to enforced SU(6) symmetry in random phase approximation.

Explicit construction of Dyson, Holstein-Primakoff, and Schwinger representations for random-phase approximation phonon operators is given within Lie algebraic framework. It is shown that these representations emerge as exact boson realizations of quadrupole collective algebra, but the enforcement of SU(6) symmetry involves important constraints embodied in definite nonlinear conditions imposed on random-phase approximation phonon amplitudes. The constructed Schwinger representation could be employed to provide alternative approach to the interacting boson model parameters, avoiding standard procedures of mapping the shell-model SD subspace into the sd boson space.

A theoretical model for structure-borne excitation of a beam and a ring in rolling contact

This paper presents a model which describes the structure-borne sound behaviour of a beam and a ring in rolling contact. By using point impedances the model is restricted to the area of the contact point. A further restriction is the consideration of the vertical direction of vibration only. In the model the main source of excitation is a force source. For the calculation of the force the original profile of the tread roughness, influenced- by the geometry of the rolling body as it picks up this roughness, is transformed into a so-called equivalent roughness with which the rolling body collides within a certain observation interval, producing a mean impulse. At the impact point the Hertzian elastic impact laws are applied so that the force-time history as well as the force spectrum can be calculated. Together with the theoretical transfer functions ( F/v ) of the model a precalculation of the structure-borne sound amplitudes excited during the rolling process becomes possible. Initial dimensions needed are the following: data on the point input impedances of the unloaded rolling body and track; data on the loss factor of the rolling process; data on the rolling body mass, contact geometry; material properties and rolling speed; data on the respective tread roughness. The method was validated by using an experimental combination of a hollow steel cylinder which rolls on two steel beams. The model also permits investigation of parameters which influence the noise behaviour during the rolling process. By means of an approximate representation of a wheel and rail as a ring and beam the model can also be applied to a wheel/rail system, and the results can be evaluated. The model is an approximation. It is not an exact realization of the actual physical process of rolling. Questions of radiation of airborne sound are not part of this study.

An exact realization of the Kac-Moody algebra

The Kac-Moody generators are explicitly realized as functional differential operators expressed in terms of the coordinates of the (infinite-dimensional) group manifold. As an application of this realization, the two-dimensional Wess-Zumino chiral action is derived from the hamiltonian formulation.

Flowgraph synthesis of Darlington - Cauer switched- capacitor filters

The Darlington-Cauer method of transfer function synthesis is proposed for the exact realization of low passband sensitivity SC filters directly from z -domain specifications. The Darlington-Cauer technique is unattractive for passive realizations due to its reliance upon ideal transformers; however, such elements are simple to realize in SC form. The resulting circuits are completely parasitic free. The use of balanced output operational amplifiers results in an economical realization.

Universal approximations of discrete-time control systems over finite time

We present an algorithm for obtaining approximate internal descriptions for a discrete-time control system, given a finite number of external experiments (input-output data). The system is required only to be causal, with a continuous input-output map. The experiments should be done in a prescribed way, with bounded inputs acting over a finite period of time. The approximation will be valid over the ranges of inputs and time covered by the experiments. The algorithm can be considered as an exact partial realization procedure for state-affine systems. An e-stable computer program will be sketched.

MFIR filters: Properties and applications

The class of multiplicative FIR (MFIR) filters is considered and some properties and applications of MFIR filters are investigated. MFIR filter approximation of a given IIR filter is shown to reduce the number of multiplications and additions logarithmically, in comparison to the corresponding FIR filter in direct form. The pure multiplicity property is introduced and is shown to apply to a class of MFIR filters. This property results in a criterion for optimal ordering and expressions for roundoff noise when no scaling is used and also results in the invariance of roundoff noise output under l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -scaling. Linear phase MFIR filter realization of a desired low-pass frequency response magnitude <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|H_{d}|</tex> with centered transition band is shown to require <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0(n \log_{2} N)</tex> each multipliers and adders. N is the order of the min-max FIR filter design of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|H_{d}|</tex> and n is the order of the elliptic IIR filter design of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|H_{d}|^{1/2}</tex> . Several design examples of linear phase low-pass filters are used to compare MFIR filter designs versus those of min-max FIR filters in direct form. Comb filters of order N are shown to have an exact MFIR realization that requires fewer than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 \log_{2} N</tex> additions. Suggestions for further research and applications conclude the paper.

Schur recursions, error formulas, and convergence of rational estimators for stationary stochastic sequences

An exact and approximate realization theory for estimation and model filters of second-order stationary stochastic sequences is presented. The properties of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> -lossless matrices as a unifying framework are used. Necessary and sufficient conditions for the exact realization of an estimation filter and a model filter as a submatrix of a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> -lossless system are deduced. An extension of the so-called Schur algorithm yields an approximate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> -lossless realization based on partial past information about the process. The geometric properties of such partial realizations and their convergence are studied. Finally, connections with the Nevanlinna-Pick problem are made, and how the techniques presented constitute a generalization of many aspects of the Levinson-Szegö theory of partial realizations is shown. As a consequence generalized recursive formulas for reproducing kernels and Christoffel-Darboux formulas are obtained. In this paper the scalar case is considered. The matrix case will be considered in a separate publication.

Lossless chain scattering matrices and optimum linear prediction: The vector case

AbstractIn this paper we give a systematic treatment of the exact and approximate realization of a positive real matrix‐valued function on the open unit disc by means of a lossless circuit connected to a passive load. We discuss the mathematical properties of the chain scattering matrix which describes the lossless circuit and rederive a form of the classical Darlington synthesis theorem generalized to roomy matrix‐valued transmission functions. We then develop a matrix version of an algorithm due to Schur for the construction of approximate realizations which produces (minimal degree) Nevanlinna–Pick approximants to the original positive real matrix. We further identify the normalized inverse of one of the outer factors of the approximant to the positive real matrix as the orthogonal projection of the identity onto a suitably defined subspace, give its interpretation as a reproducing kernel, and establish strong convergence under mild conditions on the growth of the order of the approximation. Finally we interpret and apply the mathematical theory developed in the body of the paper to the theory of prediction for vector‐valued second order stationary stochastic sequences and briefly discuss connections with the theory of maximum entropy extensions and of inverse scattering.

Collett-Wolf sources and multimode lasers

It is shown than an exact realization of a Collett-Wolf source is given by a laser oscillating on a suitable superposition of (infinitely many) transverse modes. Good approximation can be obtained with a finite number of modes.

Exact computer realization of certain computational algorithms

The question of organizing calculations in supermany-valued arithmetic on a computer is examined. A program is presented for a model computer based on a computer of type M-20, permitting the exact solution of a system of a system of linear algebraic equations to be obtained by the Gauss-Jordan method.

Realization of Elliptic Function Bandstop Filters by Means of a Resonated Prototype

Elliptic function bandstop filter realizability is normally improved by the use of a resonated prototype. It is indicated that if unit element transforms are performed before the bandstop transform is performed, a simpler procedure results, as well as exact realizations for cases of N = 5 or higher.

An operational analysis of the space-time structure

We discuss the concepts related to space-time in a quantum-relativistic theory by means of the analysis of the physical procedures used to construct a new frame of reference starting from a pre-existent frame (transformation procedures). The physical objects which form a frame of reference are allowed to interact with the other physical objects and follow the laws of quantum physics. We suggest that there are conceptual limitations which do not permit the exact realization of a transformation of the Poincaré group by means of physical procedures. We remark also that the operations performed in order to construct a frame of reference perturb the surrounding physical objects and are influenced by them. We propose some general theoretical schemes which take these facts into account and permit the separation of the geometrical effects of a transformation procedure from the physical ones. Finally we find the conditions which permit the construction of a Poincaré-invariant theory of the usual kind by means of the introduction of some ideal concepts which have no direct operational meaning.

Characteristic equation and stable states of flipflops

Stable states of flipflops can be determined from algebraic solutions of a characteristic equation. A short discussion of the four CS-flipflops leads to the Earle latch. There are two Earle latch realizations—one is an approximate realization with metastable states and the other is an exact realization with no metastable states. Realization is by delay-free gates and logical delayors. The generality enables application to the ST-flipflops widely used as an element of data shift registers.

Exact realisation of 2-dimensional digital filters by separable filters

A scheme for the exact realisation of 2-dimensional digital filters by using separable filters is proposed. The desired impulse response is obtained by a process of successive corrections. The performance criterion in terms of computing speed is compared with that of another existing technique.

Approximate linear realizations of given dimension via Ho's algorithm

Ho's Algorithm generates exact realizations of finite-dimensional linear systems, given exact data. We discuss here a variant of the algorithm that generates approximate realizations of specified dimension from approximate data.

Parameter estimation using splines

In this paper the estimation of unknown, time-invariant parameters that, if known, completely specify a discrete, linear dynamic model with Gaussian disturbances, is considered. Following the Bayesian approach the unknown parameters are modeled as random variables with known a priori probability density. Optimal, in the mean-square-error sense, estimates are desired. However, this requires recursive updating and storage of a non-Gaussian, and more importantly, a nonreproducing density. Therefore, exact realization of the nonlinear parameter estimators requires immense computational effort and storage capacity. To alleviate these difficulties, splines functions are used for the approximate realization of the Bayesian parameter estimation algorithm. Specifically, variation-diminishing splines are used, which are pieces of smoothly tied polynomials to approximate the a posteriori probability density (pdf). This approximation of the pdf is specified in terms of a finite number of parameters, yielding a readily implementable approximation of the exact but unimplementable parameter estimation algorithm. A convergence theorem is obtained for the convergence of the spline algorithm to the optimal algorithm, as well as two implementable error bounds. Extensive numerical simulation indicates that the spline algorithm performs well, yielding parameter estimates very close to the true values. In summary, the salient characteristics of the proposed spline-based estimator are as follows: 1. (a) it is readily implementable, its realization requiring essentially a bank of Kalman filters and integration of piece-wise polynomial functions; 2. (b) the spline algorithm is based essentially on an imbedded quantization algorithm, namely, the one corresponding to the bank of Karman filters used; 3. (c) as such, the spline estimator has greater computational requirements than the associated quantization algorithm; but 4. (d) the spline algorithm is more accurate than the quantization algorithm. In view of the above, the spline-based estimator should prove useful in practical applications of parameter estimation as well as of general nonlinear estimation.

Distributed RC impedances of constant phase

Exact realizations of input impedances with substantially frequency-independent phase angles over a finite frequency range are given in the form of linear distributed RC structures. The theory of these networks is outlined and some results concerning their design and performance are given.

New Design Equations for a Class of Microwave Filters (Correspondence)

New approximate design equations for a class of microwave bandpass filters are presented. The filters are 1) dual forms of half-wave parallel-coupled resonator filters, 2) one form of interdigital filter, and 3) dual forms of direct-coupled stub filters. The advantages derived from using the new equations are 1) exact realization of the specified design bandwidth and 2) improved pass-band voltage standing-wave ratio (VSWR) response in the vicinity of band edge. Experiments data are presented for a trial filter design having 7 resonators, 40-percent bandwidth, and passband VSWR of 1.2.

Symmetry properties of linear broadside arrays

Optimality properties are proved for arrays that exhibit symmetry about their geometric centers. Specifically, a symmetric array has smaller sidelobes than a nonsymmetric one; this is true not only for exact realization but, in the worst case, for inexact realization as well.

Diode and Transistor Self-Analogues for Circuit Analysis

A new method of circuit analysis based on the time-scaling of actual circuits has been proposed. Audio-frequency self-analogues of microwave frequency transistors can be constructed using charge control theory, and these accurately model transistor performance in the active region. Scaling of storage times in diodes and transistors requires multiple-lump modeling. The multiple lump model developed by Linvill is reformulated here on the basis of an analogy between charge density in the semiconductor and charge density in the model, rather than between carrier density and voltage. Only two parameters, time constants corresponding to lifetime and a diffusion transit time in the semiconductor, need be specified in the reformulated model. This simplified multiple-lump model should be generally useful for device calculations. We describe a diode self-analogue which is an exact physical realization of the multiple-lump model. Separation of active and saturation region stored charges can be achieved in a transistor self-analogue, so that a single-lump model can be used for the active, and a multiple-lump model for the saturation region stored charges.