Image Processing Reference
In-Depth Information
13
Applications of Interval-Based
Simulations to the Analysis and
Design of Digital LTI Systems
Juan A. López 1 , Enrique Sedano 1 , Luis Esteban 2 , Gabriel Caffarena 3 ,
Angel Fernández-Herrero 1 and Carlos Carreras 1
1 Departamento de Ingeniería Electrónica, Universidad Politécnica de Madrid,
2 Laboratorio Nacional de Fusión, Centro de Investigaciones Energéticas
Medioambientales y Tecnológicas (CIEMAT),
3 Departamento de Ingeniería de Sistemas de Información y de Telecomunicación,
Universidad CEU-San Pablo,
Spain
1. Introduction
As the complexity of digital systems increases, the existing simulation-based quantization
approaches soon become unaffordable due to the exceedingly long simulation times. Thus,
it is necessary to develop optimized strategies aimed at significantly reducing the
computation times required by the algorithms to find a valid solution (Clark et al., 2005;
Hill, 2006). In this sense, interval-based computations are particularly well-suited to reduce
the number of simulations required to quantize a digital system, since they are capable of
evaluating a large number of numerical samples in a single interval-based simulation
(Caffarena et al., 2009, 2010; López, 2004; López et al., 2007, 2008).
This chapter presents a review of the most common interval-based computation techniques,
as well as some experiments that show their application to the analysis and design of digital
Linear Time Invariant (LTI) systems. One of the main features of these computations is that
they are capable of significantly reducing the number of simulations needed to characterize
a digital system, at the expense of some additional complexity in the processing of each
operation. On the other hand, one of the most important problems associated to these
computations is interval oversizing (i.e., the computed bounds of the intervals are wider
than required), so new descriptions and methods are continuously being proposed. In this
sense, each description has its own features and drawbacks, making it suitable for a
different type of processing.
The structure is as follows: Section 2 presents a general review of the main interval-based
computation methods that have been proposed in the literature to perform fast evaluation of
system descriptions. For each technique, the representation of the different types of
computing elements is given, as well as the main advantages and disadvantages of each
approach. Section 3 presents three groups of interval-based experiments: (i) a comparison of
the results provided by two different interval-based approaches to show the main problem
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