A Transformation Algorithm for Estimating System Laplace Transform from Sampled Data

On the Stability of 2-D Continuous Systems

The discrete Lotka power function describes the number of sources (e.g., authors) with n = 1, 2, 3, … items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It is, hence, important to know the relations between the two models. We show that the exponents of the discrete Lotka function (if not too high, i.e., within limits encountered in practice) and of the continuous Lotka function are approximately the same. This is important to know in applying theoretical results (from the continuous model), derived from practical data.

Gain-margin based discrete-continuous method for the stability analysis of real-time hybrid simulation systems

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

The realization of fractional-order controllers is based on the approximation of the irrational operators by continuous or discrete transfer functions. However, at high sampling frequencies, discrete z-transfer functions approximations can be very sensitive even to small changes in coefficient values. This technical note proposes a realization of sν , in terms of transfer functions in the complex delta-domain, which improves considerably the robustness of the approximation to parameter changes and then to truncation in transfer function coefficients applied for implementation with finite word length.

One confusing question over a long period of time is how transfer the discrete function transfers into continuous function. Recently the issue has been resolved but some details of the transformation process will be introduced in the paper. The correlation coefficients of 100,000 values are established from the two groups of data with the range between -1 and 1, creating a histogram from these correlation coefficient values known as “the probability mass function.” The coefficient values are brought into the discrete distribution function, so that transfers into the discrete cumulative function, next converted into a continuous cumulative function, next which is differentiated to get the density function, so that it is easy to being research analysis. A model will be established during the process of the conversion what the medium is “the least squares algorithm.” Finally, when the integral of the area within the range of the density function equals to 1, this implies that the transformation complete succeeds from the discrete function to the continuous function.

Discrete linear uniformly sampled digital filters are often employed in situations where there exists some preliminary linear analog continuous filtering operation. The latter continuous filter transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P(s)</tex> is usually a low-pass function that is required for such purposes as reducing the effects of aliasing, limiting the dynamic range of the signal prior to digitization, etc. The realization of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P(s)</tex> is usually achieved quite independently of the realization of the subsequent discrete transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(z)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z = e^{sT}</tex> . In this contribution, it is shown that maximally flat solutions exist for the composite transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P(s) \cdot H(z)</tex> , so that it is possible to employ a simple baseband prefiliter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P(s)</tex> which, combined with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(z)</tex> , results in an overall maximally flat low-pass response.

An efficient two-dimensional finite-element (FE) model is developed for the calculation of synchronous machine transfer functions. The numerical model uses two equivalent sinusoidally distributed stator windings substituting the actual three-phase machine by an equivalent two-phase one, leading to simplified FE simulations. Just two complex solutions per frequency are needed to obtain the three transfer functions that completely describe the two-port nature of the d axis network. A new FE-based method is proposed to accurately establish the rotor base quantities, allowing the calculated transfer functions to be in per-unit. Results are validated by comparing the performance of a two-axis equivalent circuit, derived from the FE transfer functions, with a reference transient FE program.

This paper presents theory for multivariable system identification using matrix fraction descriptions and the matrix continued fraction description approach which, in turn, yields a lattice-type order-recursive structure. Once the matrix continued-fraction expansion has been determined, it is straightforward to obtain solutions to both the left and right coprime factorizations of transfer function estimates and, in addition, solution to problems of state estimation (observer design) and pole-assignment control. An important and attractive technical property is that calculation of transfer functions in the form of right and left coprime factorizations, calculation of state variable observers and regulators all can be made using causal polynomial transfer functions defined by means of matrix sequences of the continued-fraction expansion applied in causal and stable forward-order and backward-order recursions. >

Due to the changes which may occur in their parameters, systems are usually demonstrated by some subsystems for different conditions. This paper employs Modified Petri Nets (MPN) to model theses subsystems and makes it simple to analyze them. In this method, first, the continuous transfer function is converted to a discrete transfer function and then, by MPN, system is modeled and analyzed. All subsystems can be modeled and used in state control or cascade control loops. Here, the focus is mainly on the conception as well as the definitions of the new unified representation model for continuous control systems. Simulation results show that the new method for modeling continuous systems works effectively.

A methodology for the simulation of bandpass continuous time sigma-delta (SigmaDelta) modulators is presented in this paper. This method permits the simulation of SigmaDelta modulators employing continuous-time filters using a fixed-step algorithm. The method is based on the discretization of a continuous-time model and the use of a discrete simulator, which is more efficient than an analog simulator. This transformation is exact in term of noise transfer function and asymptotically exact in term of signal transfer function (the signal transfer function of the model rapidly tends to the continuous time model transfer function when the number of steps increases).

This special issue of the VLSI DESIGN: an International Journal of Custom-Chip Design, Simulation and Testing is devoted to spectral techniques, new types of decision trees and diagrams, their applications, efficient ways of their calculation and mutual relations between spectral techniques and classical decision diagrams. Manipulations and calculations with discrete functions are fundamental tasks in many areas of Computer Science and Engineering. Many problems in digital system design, simulation and testing can be expressed as a sequence of operations on discrete functions. The performance of Computer-Aided Design systems used in solving various problems in this area strongly depends on the efficiency of representations of discrete functions. Decision Diagrams (DDs) have proved very convenient data structure for discrete function representations, permitting manipulations and calculations with large functions efficiently in terms of time and space. In many applications, as for example those involving large matrices, conventional algorithms are significantly improved by using DDs. In logic design, such applications relate to basic problems of the design, verification, simulation and testing logical networks. Besides Boolean functions, some other types of discrete representations, such as multi-valued functions, cube sets, EXOR-based spectral and probabilistic formulas have to be dealt with. Hence the numbers of different decision trees and diagrams have been introduced for these various applications and representations. The spectral or polynomial representation of Boolean function is obtained by expressing it in terms of an orthogonal basis. The most popular basis is formed by discrete Walsh functions. Note that the spectral and the polynomial representation of a Boolean function are equivalent. The discrete orthogonal functions are referred to as the basis functions when the spectral or abstract harmonic terminology is used and as monomials when the polynomial terminology is used. Such polynomial representations have extensive applications in coding theory and cryptography as well as design of nonlinear filters. Spectral techniques based on Walsh, Haar, Arithmetic and Reed–Muller transforms have been used in digital logic design for more than 30 years. These techniques have been used for Boolean function classification, disjoint decomposition, identification of symmetries, parallel and serial linear decomposition, spectral translation synthesis (extraction of linear preand post-filters), multiplexer synthesis, threshold logic synthesis, state assignment and testing, and evaluation of logic complexity. The renewed interest in applications of spectral methods in design of VLSI digital circuits is caused by their excellent design for testability properties and in their efficiency in Boolean mapping problems. Furthermore, the practical applicability of these techniques was greatly improved with the development of efficient methods that allow calculating and operating on spectra of Boolean functions directly from reduced representations of such functions in the form of arrays of cubes or decision diagrams. Following from these recent developments, techniques have been presented for efficient spectral translation to decompose a circuit into a cascade of two sub circuits: linear block composed of EXOR gates fed by the primary input of the overall circuit. Such linear decomposition drastically simplifies the synthesis task. The choice of suitable linear transformation is based on a complexity measure assigned to each Boolean function that is heuristically related to the complexity of the final circuit implementation. To avoid the experimental costs of computing the Walsh transform, Binary Decision Diagrams (BDDs) based techniques are used. Recently the idea of linear transformations is applied to decision diagrams. By combining powerful spectral linear techniques with variable reordering techniques, it is possible to synthesize large Boolean functions with standard Computer-Aided Design tools that fail otherwise. The areas addressed by this special issue span spectral transforms, their applications and efficient calculation methods through decision diagrams. New spectral decision diagrams are also emerging that support larger data structures allowing more complex discrete representations to be implemented that was previously impossible.

A simple and straightforward procedure for the realization of multidimensional digital filters which are based on the concept of generalized immittance converter is presented. It is known that these digital filters possess many salient features such as low noise, low sensitivity, absence of limit cycles and capability of realizing multiple transfer functions. Unlike the other known methods, which use analog transfer function as the basis, the method proposed in this paper uses the discrete transfer function directly for realization. It is shown that the required details of the resulting filter structure, namely, the organization of the different adaptors and the values of the multiplier constants can be obtained directly from the specified discrete transfer function.

Number of software Reliability growth models has been proposed in the literature. A mathematical technique which describes the software testing phenomenon known as the software reliability growth model. Software reliability growth models are used to predict the number of faults and reliability of the software. In the view of this software reliability growth models are basically differentiated as the continuous and discrete models. There is a plenty of development in the continuous models but little towards the discrete models. In this paper we have presented a discrete reliability growth model with different discrete testing effort functions and the same time software release policy is discussed. A new imperfect debugging discrete software reliability growth model with testing effort is proposed. All calculations are done on real data. The results shows the proposed testing effort models are perfectly fit to the data.

In this paper we propose a novel fast algorithm for calculating the transfer function of the Zelinski post-filter in a microphone array. The proposed algorithm requires less memory and fewer arithmetical multiplications. We demonstrate that for the “classical” algorithm computational complexity increases quadratically as a function of the number of microphones in the array. In contrast, the computational complexity of the proposed algorithm increases linearly. This provides a considerable acceleration in the calculation of the post-filter transfer function in real-time systems.