Global Positioning System Reference
In-Depth Information
Signals and Systems
The concepts of a signal and a system are crucial to the topic of this topic. We
will consider time as well as frequency domain models of the signals. We focus
on signals and system components that are important to study software-defined
GPS and Galileo receiver design. For a detailed treatment of signal and system
theory, we refer to the many standard signal processing textbooks on the market.
1.1
Characterization of Signals
In satellite positioning systems, we encounter two classes of signals referred to as
deterministic and random signals. Deterministic signals are modeled by explicit
mathematical expressions. The signals
x
5
e
50
t
are
examples of deterministic signals. A random signal, on the other hand, is a signal
about which there is some degree of uncertainty. An example of a random signal is
a received GPS signal: the received signal contains beside the information bearing
signal also noise from disturbances in the atmosphere and noise from the internal
circuitry of the GPS receiver; see Chapter 4 for more details.
Now some basic topics on deterministic and stochastic signal theory are re-
viewed and simultaneously we establish a notation.
A reader familiar with
random processes
knows concepts like autocorrelation
function, power spectral density function (or power spectrum), and bandwidth.
These concepts can be applied for deterministic signals as well, and that is ex-
actly what we intend to do in the following. There are several good sources about
random processes; see, for example, Strang & Borre (1997), Chapter 16.
(
t
)
=
10 cos
(
100
t
)
and
x
(
t
)
=
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