Linearization of Time-Varying Nonlinear Systems Using A Modified Linear Iterative Method

The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented. To this end, an alternative view on the Volterra series is established, which enables the utilization of certain modified linear iterative methods for linearization. For one particular linear iterative method, the Richardson iteration, the corresponding post- and pre-linearizers are discussed in detail. It is motivated that the resulting algorithm can be regarded as a generalization of some existing methods. Furthermore, a simply verifiable condition for convergence is presented, which allows the straightforward evaluation of applicability. The proposed method is demonstrated by means of the linearization of a time-varying nonlinear amplifier, which highlights its capability of linearizing significantly distorted signals, illustrates the advantageous convergence behavior, and depicts its robustness against modeling errors

Linearization of analytic and non--analytic germs of diffeomorphisms of (C,0)({\mathbb C},0)

We study Siegel's center problem on the linearization of germs of diffeomorphisms in one variable. In addition of the classical problems of formal and analytic linearization, we give sufficient conditions for the linearization to belong to some algebras of ultradifferentiable germs closed under composition and derivation, including Gevrey classes. In the analytic case we give a positive answer to a question of J.-C. Yoccoz on the optimality of the estimates obtained by the classical majorant series method. In the ultradifferentiable case we prove that the Brjuno condition is sufficient for the linearization to belong to the same class of the germ. If one allows the linearization to be less regular than the germ one finds new arithmetical conditions, weaker than the Brjuno condition. We briefly discuss the optimality of our results.Comment: AMS-Latex2e, 11 pages, in press Bulletin Societe Mathematique de Franc

Linearization of CIF Through SOS

Linearization is the procedure of rewriting a process term into a linear form, which consist only of basic operators of the process language. This procedure is interesting both from a theoretical and a practical point of view. In particular, a linearization algorithm is needed for the Compositional Interchange Format (CIF), an automaton based modeling language. The problem of devising efficient linearization algorithms is not trivial, and has been already addressed in literature. However, the linearization algorithms obtained are the result of an inventive process, and the proof of correctness comes as an afterthought. Furthermore, the semantic specification of the language does not play an important role on the design of the algorithm. In this work we present a method for obtaining an efficient linearization algorithm, through a step-wise refinement of the SOS rules of CIF. As a result, we show how the semantic specification of the language can guide the implementation of such a procedure, yielding a simple proof of correctness.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Power amplifier memory-less pre-distortion for 3GPP LTE application

A new and simple Power Amplifier (PA) linearization method is proposed and demonstrated using a very high efficiency yet inherently nonlinear inverse class-F PA. This was conducted in the presence of a generic variable envelope RF signal in order to extract its AM-AM and AM-PM characteristics. Deducing the polynomial pre-distortion parameters from the AM-AM and AM-PM characteristic has resulted in the successful linearization of the PA in the presence of 3GPP Long Term Evolution (LTE) signals. The results obtained for the PA - a 12W GaN HEMT inverse Class-F structure designed to operate at 900MHz - demonstrate the proof of concept and the efficiency of the proposed linearization technique with significant advantageous reduction in base-band resources for 3GPP LTE applications.A new and simple power amplifier (PA) linearization method is proposed and demonstrated using a very high efficiency yet inherently nonlinear inverse class-F PA. This was conducted in the presence of a generic variable envelope RF signal in order to extract its AM-AM and AM-PM characteristics. Deducing the polynomial pre-distortion parameters from the AM-AM and AM-PM characteristic has resulted in the successful linearization of the PA in the presence of 3GPP long term evolution (LTE) signals. The results obtained for the PA - a 12 W GaN HEMT inverse class-F structure designed to operate at 900 MHz - demonstrate the proof of concept and the efficiency of the proposed linearization technique with significant advantageous reduction in base-band resources for 3GPP LTE applications

Concurrent Data Structures Linked in Time

Arguments about correctness of a concurrent data structure are typically carried out by using the notion of linearizability and specifying the linearization points of the data structure's procedures. Such arguments are often cumbersome as the linearization points' position in time can be dynamic (depend on the interference, run-time values and events from the past, or even future), non-local (appear in procedures other than the one considered), and whose position in the execution trace may only be determined after the considered procedure has already terminated. In this paper we propose a new method, based on a separation-style logic, for reasoning about concurrent objects with such linearization points. We embrace the dynamic nature of linearization points, and encode it as part of the data structure's auxiliary state, so that it can be dynamically modified in place by auxiliary code, as needed when some appropriate run-time event occurs. We name the idea linking-in-time, because it reduces temporal reasoning to spatial reasoning. For example, modifying a temporal position of a linearization point can be modeled similarly to a pointer update in separation logic. Furthermore, the auxiliary state provides a convenient way to concisely express the properties essential for reasoning about clients of such concurrent objects. We illustrate the method by verifying (mechanically in Coq) an intricate optimal snapshot algorithm due to Jayanti, as well as some clients

Spurious Welfare Reversals in International Business Cycle Models

Several papers on international business cycles have documented spurious welfare reversals, in that incomplete market economies can produce higher welfare than the complete market economy. This paper demonstrates how conventional linearization, as used in King, Plosser, and Rebelo (1988), can generate approximation errors that are large enough to result in such reversals. Using a two-country production economy without capital, we argue that spurious welfare reversals are not only possible but also plausible under reasonable parameter values. As a constructive alternative, this paper proposes an approximation method that modifies the conventional linearization method by a bias correction---the linear approximation around a 'stochastic' steady state. We show that this method can be easily implemented to accurately approximate the exact solution and therefore produce the correct welfare ordering. The accuracy of the proposed method is far better than that of the conventional linearization method and as good as that of a method involving a second-order expansion.Linearization, Stochastic steady state, Welfare, Risk sharing