Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

Saving, productivity and national income: a discrete-time geometric framework

This paper proposes an alternative geometric framework for analysing the inter-relationship between domestic saving, productivity and income determination in discrete time. The framework provides a means of understanding how low saving economies like the United States sustained high growth rates in the 1990s whereas high saving Japan did not. It also illustrates how the causality between saving and economic activity runs both ways and that discrete changes in national output and income depend on both current and previous accumulation behaviour. The open economy analogue reveals how international capital movements can create external account imbalances that enhance income growth for both borrower and lender economies. (C) 2002 Elsevier Science B.V. All rights reserved.

Finite difference time domain (FDTD) method for modeling the effect of switched gradients on the human body in MRI

Numerical modeling of the eddy currents induced in the human body by the pulsed field gradients in MRI presents a difficult computational problem. It requires an efficient and accurate computational method for high spatial resolution analyses with a relatively low input frequency. In this article, a new technique is described which allows the finite difference time domain (FDTD) method to be efficiently applied over a very large frequency range, including low frequencies. This is not the case in conventional FDTD-based methods. A method of implementing streamline gradients in FDTD is presented, as well as comparative analyses which show that the correct source injection in the FDTD simulation plays a crucial rule in obtaining accurate solutions. In particular, making use of the derivative of the input source waveform is shown to provide distinct benefits in accuracy over direct source injection. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and the source injection method has been verified against examples with analytical solutions. Results are presented showing the spatial distribution of gradient-induced electric fields and eddy currents in a complete body model.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Review of time-domain polarization measurements for assessing insulation condition in aged transformers

This paper presents a review of the time-domain polarization measurement techniques for the condition assessment of aged transformer insulation. The polarization process is first described with appropriate dielectric response theories and then commonly used polarization methods are described with special emphasis on the most widely used return voltage(rv) measurement. Most recent emphasis has been directed to techniques of determining moisture content of insulation indirectly by measuring rv parameters. The major difficulty still lies with the accurate interpretation of return voltage results. This paper investigates different thoughts regarding the interpretation of rv results for different moisture and ageing conditions. Other time domain polarization measurement techniques and their results are also presented in this paper.

Constructing good deals in discrete time arbitrage-free dynamic pricing models

Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Fractional discrete-time signal processing: scale conversion and linear prediction

Nonlinear Dynamics, Vol. 29

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

Time-domain optimization of amplifiers based on distributed genetic algorithms

Thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Electrical and Computer Engineering

Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Impedance boundary conditions for pseudo-spectral time-domain methods in room acoustics

The pseudo-spectral time-domain (PSTD) method is an alternative time-marching method to classicalleapfrog finite difference schemes in the simulation of wave-like propagating phenomena. It is basedon the fundamentals of the Fourier transform to compute the spatial derivatives of hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acoustics simulations. However, one of the first issues to be solved consists on modeling wallabsorption. Unfortunately, there are no references in the technical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals to overcome this problem are presented, validated and compared to analytical solutions in different scenarios.