This chapter considers the approximation of the transfer function of a linear system in terms of a causal filter bank. Assume that \(f\left( {{\rm{e}}^{{\rm{i}}\theta } } \right)\) with \(\theta \in [-\pi,\pi)\) is the transfer function of an arbitrary discrete-time linear system \({\cal L}\), and let \(\Phi = \left\{ {\varphi _k } \right\}_{k = 1}^\infty \) be a set of transfer functions of an orthonormal filterbank. It is assumed that f as well as all \(\varphi_{k}\) are elements of a certain Banach algebra \({\cal B}\) which characterizes the system theoretical properties of \({\cal L}\) and of the filterbank \(\Phi \). Moreover, since f as well as \(\{\varphi_{k}\}^{\infty}_{k=1}\) should represent causal systems, these transfer functions have to belong to the causal subspace \({\cal B}_ + \,{\rm{of}}\,{\cal B}\). Then, it is desirable to obtain an approximation of f in this filterbank of the form
Transfer function estimation of turboalternator from practical operating data by spectral analysis
Transfer function estimation of turboalternator from practical operating data by spectral analysis
On the quasi-central elements of Banach algebras
In the eighties of the last century Rennison studied and characterized the set of quasi-central elements of some unital Banach algebras. In this paper, we improve one of Rennison's result assert that for given unital Banach algebra \(A\) the set of quasi-central elements \(Q(A)\), need not be equal to centre of \(A\) and need not be closed under addition or multiplication. Further, we prove that if \(A\) is unital ultraprime Banach algebra, then \(Q(A)\) need not be equal to centre of \(\mathrm{A}\) and need not be closed under addition or multiplication.
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9On the dynamic system identification of the response behaviour of linear viscoelastic materials
On the dynamic system identification of the response behaviour of linear viscoelastic materials
A method of determining the transfer function of a linear system in terms of its pol es and zeros from the frequency response
A procedure is developed for obtaining the transfer function of a linear system from the frequency-response data in terms of its poles and zeros. The method is based upon the fact that the transfer function is an analytic function of the complex variable s at all points in the s plane except the isolated points which are the poles of the function. Hence if the function is specified along the jω axis, it is possible to extend the function in the left-half or right-half s plane by means of conformai mapping techniques. The curvilinear squares in the G(s) plane corresponding to a grid of constant σ and constant ω lines in the s plane can be constructed with fair accuracy after a little practice. The particular values of σ and ω, for which the lines pass through the origin of the s plane, can thus be determined by locating the zeros of the transfer function. The poles are similarly obtained by working with the inverse function. Since there are several values of s satisfying G(s) = 0, the mapping from the s plane to the G(s) plane is not entirely a one-to-one mapping, and several regions in the s plane are mapped on to the same region in the G(s) plane. A method is suggested to overcome this difficulty and to obtain, step-by-step, all the zeros and poles of the transfer function corresponding to the given frequency-response locus. The method is illustrated by means of three numerical examples.
Read moreاستفاده از تحلیل آماری افت‌وخیزهای ناهمبسته برای شناسایی سامانه‌های آشکارسازی هسته‌ای حالت پالسی
یکی از فرایندهای تصادفی که در اکثر آزمایش‌های هسته‌ای مشاهده می‌شود، فرایند تصادفی پواسون است. با توجه به اثر زمان‌مرده در سامانه‌های آشکارسازی حالت پالسی، فرایند اندازه‌گیری شده در خروجی آشکارساز نسبت به فرایند تصادفی پواسون دارای اعوجاج است. در این تحقیق با استفاده از روش‌های تحلیل آماری به شناسایی سامانه‌های آشکارسازی حالت پالسی پرداخته شده است. یکی از آشکارسازهای نوعی که در حالت پالسی کار می‌کند، آشکارساز BF3 است. در این پژوهش یک آشکارساز BF3 نوعی برای پیاده‌سازی روش فوق انتخاب شد و سپس پالس‌های مشاهده شده در خروجی آشکارساز در حوزه زمان با استفاده از تحلیل آماری افتوخیزها اندازه‌گیری و تحلیل گردید. در آزمایش‌هایی مانند اندازه‌گیری‌های مربوط به تئوری نوفه رآکتور قدرت صفر، تابع انتقال سامانه آشکارسازی استفاده شده نیز خود بر نتایج به‌دست آمده اثرگذار است. از این‌رو آگاهی از تابع انتقال سامانه آشکارسازی به‌کار گرفته شده در این آزمایش‌ها از اهمیت ویژه‌ای برخوردار است. همچنین، در اندازه‌گیری‌هایی که در آنها تصحیح زمان‌مرده سامانه آشکارسازی ضروری است، مشخص بودن تابع انتقال می‌تواند اطلاعات مفیدی از اثرات زمان‌مرده را در اختیار قرار دهد. در این پژوهش تابع انتقال یک سامانه آشکارسازی نوترون نوعی که بر پایه‌ی آشکارساز BF3 است بررسی شده است.
Read more9Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks
This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates. Based on the stationary phase method, the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.
Read more12On Padé-type model order reduction of J-Hermitian linear dynamical systems
On Padé-type model order reduction of J-Hermitian linear dynamical systems
17Transfer functions of discrete-time nonlinear control systems; 322-335
The notion of the transfer function of the discrete-time nonlinear control system is defined. The definition is based on a non-commutative twisted polynomial ring, which can be by the Ore condition extended into its quotient ring (field of fractions). Some properties of the transfer function, related to accessibility and observability of the system, are studied and the transfer functions of different composite systems (series, parallel, and feedback connections) are given. The resulting theory is, in principle, similar to that in the linear case, except that the polynomial description relates now the differentials of inputs and outputs, and the resulting polynomial ring is non-commutative.
Read more3A low‐dimensional realization algorithm for periodic input/output behavioral systems
The state‐space realization of linear systems is of utmost importance in linear systems theory. After the realization problem for the time‐invariant case was solved, particular attention was paid to the case of linear periodic systems. Recently, such systems have regained importance, for instance, in the context of coding theory where periodic convolutional encoders play an important role. The majority of the contributions within this area only concern the realization of transfer functions (or impulse responses), thus excluding the case of input/output linear systems without coprime representations. By the end of the eighties of the last century, Jan C. Willems suggested an approach (nowadays known as the behavioral approach) that considers a wider class of systems and allows to overcome this drawback. According to this approach, the central object in a system is its behavior which consists of all the signals that satisfy the system laws (also called system trajectories). Consequently, the behavior of a system with an input/output representation that is not coprime contains more trajectories than the set of input/output signals defined by the system transfer function. Our work takes this fact into account. In previous research conducted by the authors, some results on the realization of periodic behavioral systems were obtained, which, despite their importance, are conservative with respect to the dimension of the obtained realizations. In this paper, we revisit the behavioral periodic realization problem and give further insight into this question. This allows to derive new results and set up an algorithm to compute low‐dimensional state‐space realizations.
Read more9Additive property of pseudo Drazin inverse of elements in Banach algebras
This article concerns the pseudo Drazin inverse of the sums (resp. differences) and the products of elements in a Banach algebra A. Some equivalent conditions for the existence of the pseudo Drazin inverse of a + b (resp. a - b) are characterized. Moreover, the representations for the pseudo Drazin inverse are given. Some related known results are generalized.
Read moreModeling of an active suspension system of a quarter car model via parametric system identification methods
In this study, transfer function of an active suspension system of a quarter car model is modeled via parametric system identification methods. It is tried to obtain a method that can provide the best representation of the transfer function of the system by utilizing different transfer function modeling tools. Most of mechanical systems include active suspension system of a quarter car model are modeled as mass spring damping systems. Proposing the best system identification method that represents the transfer function model of a system examined in this study is a crucial task to make a generalization for modeling of these type of systems. Numerical simulation studies are realized in Matlab environment to observe the performances of these methods and present them in a comparative manner. As a result of these simulations it is observed via the comparative results that Output Error (OE) transfer function model is an useful system identification tool for the mentioned purpose.
Read more1Steady-state, harmonic response and moments of linear systems with periodic jumps
Steady-state, harmonic response and moments of linear systems with periodic jumps
28Spectral properties of elements in different Banach algebras
Let A be a Banach algebra with unit 1 and let B be a Banach algebra which is a subalgebra of A and which contains 1. In [5]Barnes gave sufficient conditions for B to be inverse closed in A. In this paper we consider single elements and study the question of how the spectrum relative to B of an element in B relates to the spectrum of the element relative to A.
Read more1Assessment of data by a second-order transfer function
A newly developed theory for predicting the response of a linear system to an electromagnetic pulse, based only on the measured continuous-wave magnitude, is applied to the problem of possible electromagnetic interferences at a sensitive part of a torpedo. The measured magnitude representing the system's transfer function is deduced first from the measured response at this sensitive point to a known cw source, supplied by the Naval Surface Warfare Center. We derive an analytic expression for the magnitude square of the transfer function to approximate the measured data and obtain a system transfer function in terms of the complex fi"equency, from which we predict the system's cw phase characteristics and its multiple solutions due to a given impulse source.
Read more3Binomial sums, moments and invariant subspaces
The main result of this paper is that if a sequence of complex numbers (an)n≥0 satisfies\(\sum\limits_{\mathop {k = 0}\limits_{k even} }^n {\left({_k^n } \right)a_k = O(n^r)} \)and % MathType!MTEF!2!1!+-\(\sum\limits_{\mathop {k = 0}\limits_{k odd} }^n {\left({_k^n } \right)a_k = O(n^r )} as n \to \infty,\) for some integerr≥0, thenan=0 for alln>r. As an application, we deduce a localized form of a theorem of Allan about nilpotent elements in Banach algebras, and this in turn leads to an invariant-subspace theorem. As a further application, we prove a variant of Carleman's theorem on the unique determination of probability distributions by their moments. The paper concludes with a quantitative form of the main result.
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