Digital Signal Processing Reference
In-Depth Information
where
f(t)
is the force applied to the mass
M
and
x(t)
is the resulting displacement
of the mass.
A second physical phenomenon to be modeled is called
signals
.
Physical sig-
nals
are modeled by
mathematical functions
. One example of a physical signal is the
voltage that is applied to the speaker in a radio. Another example is the tempera-
ture at a designated point in a particular room. This signal is a function of time be-
cause the temperature varies with time. We can express this temperature as
temperature at a point = u(t),
(1.3)
where has the units of, for example, degrees Celsius.
Consider again Newton's second law. Equation (1.2) is the
model
of a physical
system, and and are
models
of physical signals. Given the signal (function)
, we solve the model (equation) (1.2) for the signal (function) . In analyzing
physical systems, we apply mathematics to the
models
of systems and signals, not to
the physical systems and signals. The usefulness of the results depends on the accu-
racy of the models.
In this topic, we usually limit signals to having one independent variable. We
choose this independent variable to be
time, t
, without loss of generality. Signals are
divided into two natural categories. The first category to be considered is
continuous-
time,
or simply,
continuous, signals
. A signal of this type is defined for all values of
time. A continuous-time signal is also called an
analog signal
. A continuous-time
signal is illustrated in Figure 1.2(a).
u(t)
f(t)
x(t)
f(t)
x(t)
Amplitude
0
t
(a)
Amplitude
4
T
5
T
T
0
T
2
T
3
T
6
TnT
Figure 1.2
(a) Continuous-time signal;
(b) discrete-time signal.
(b)
