In this chapter, I present a specific view of signal processing. I provide the basic definitions regarding what - according to our view - signal processing should be seen as, and I elucidate in this perspective the meaning of a selection of relevant algorithms and approaches.

When a system becomes unstable or noise becomes excessive, often regulations of the form of limiters (barriers obstructing excursion into undesired areas of the phase space) are imposed. It is hoped that by the influence of this element, the system can be calmed and its behaviour can be...

Many dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the...

In this chapter, we first precise the concept of dynamical systems, and then we introduce the concept of chaos, which is characterized by a sensitive dependence on initial conditions. To quantify this, dynamical (Lyapunov exponents) and probabilistic (dimensions) measures are introduced.

In this chapter, we introduce the concept of the embedding dimension, as the smallest topological dimension required to ensure that an object described by simpler (often scalar) time series can be embedded in a higher topological dimension.

FM -- Introduction -- Part I: Mathematical background -- Dynamical systems -- An example of nonlinear dynamical system: The Logistic Map -- Bifurcations -- From local bifurcations to global dynamics: Hopf systems from the applied perspective -- Chaos -- Embedding and mutual information -- Part...

This interdisciplinary book argues that the economy has an underlying non-linear structure and that business cycles are endogenous, which allows a greater explanatory power with respect to the traditional assumption that dynamics are stochastic and shocks are exogenous. The first part of this...

Household debt relative to disposable income increased from 60% in 1980 to 104% at the end of 2003. ‘Buying on credit’ has become so popular that an increasing number of firms generate more profit from financing than from selling their products. In this paper, we show that rising income...

The method Schroeder is accepted amongst real estate professionals in Switzerland as a near standard for condition monitoring, budgeting of maintenance and refurbishment, and strategic decision support in point of building portfolios. It is based on the devaluation curves of 12 or more building...

The paper revives a theoretical definition of party coherence as being composed of two basic elements, cohesion and factionalism, to propose and apply a novel empirical measure based on spin physics. The simultaneous analysis of both components using a single measurement concept is applied to...