Digital Signal Processing Reference
In-Depth Information
1
INTRODUCTION
In this topic, we consider the topics of signals and systems as related to engineer-
ing. These topics involve the
modeling
of physical signals by mathematical functions,
the
modeling
of physical systems by mathematical equations, and the solutions of the
equations when excited by the functions.
1.1
MODELING
Engineers must model two distinct physical phenomena. First,
physical systems
are
modeled by
mathematical equations
. For systems that contain no sampling
(
continuous-time,
or
analog, systems
), we prefer to use ordinary differential equa-
tions with constant coefficients; a wealth of information is available for the analysis
and the design of systems of this type. Of course, the equation must accurately
model the physical systems. An example of the model of a physical system is a linear
electric-circuit model of Figure 1.1:
t
L
di(t)
dt
1
C
L
+ Ri(t) +
i(t)dt = v(t).
(1.1)
-
q
Another example is Newton's second law,
f(t) = M
d
2
x(t)
dt
2
,
(1.2)
L
R
i
(
t
)
v
(
t
)
C
Figure 1.1
Example circuit.
1
