Chapter 2
ANALYSIS OF SPACE-TIME SIGNALS
2.1 INTRODUCTION TO SPACE-TIME PROCESSES
So far, we have considered a number of MIMO system models with time
being the only free parameter. In this chapter, these basic concepts will be
extended to signals and systems with more than one independent variable.
First, in Section 2.2, we shall develop the analytical framework for
multidimensional signals in time-domain with emphasis on spatial
coordinates representing sets of additional free parameters. As we consider
information carrying electromagnetic waves, these propagating waves are
described as functions of space and time. In mechanics, space is the
geometric region occupied by bodies [1]. Positions in space are determined
relative to some geometric reference system by means of linear and angular
measurements. We shall see how these coordinate systems can be
appropriately chosen depending on geometrical details of the problem.
Vector analysis and differential operators in orthogonal coordinate systems
are briefly reviewed and applied to the wave equations.
Then, in Section 2.3, we shall investigate electromagnetic waves and
their behavior in linear media. Propagation effects will be considered. In
Section 2.4, frequency domain representations of propagating plane waves
are introduced. Three additional frequency variables are related to the
coordinates in a chosen fixed coordinate system. In addition to the well-
known temporal frequency, we shall characterize a propagating wave by its
three spatial frequency components, represented in terms of so-called
wavenumber vectors.
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