Digital Signal Processing Reference
In-Depth Information
The second category for signals is
discrete-time,
or simply,
discrete, signals
. A
discrete signal is defined at only certain instants of time. For example, suppose that
a signal is to be processed by a digital computer. [This operation is called
digital
signal processing
(DSP).] Because a computer can operate only on numbers and not
on a continuum, the continuous signal must be converted into a sequence of num-
bers by sampling. If a signal is sampled every
T
seconds, the number sequence
is available to the computer. This sequence of
numbers is called a
discrete-time signal
. Insofar as the computer is concerned,
with
n
a noninteger does not exist (is not available). A discrete-time signal is illus-
trated in Figure 1.2(b).
We define a
continuous-time system
as one in which all signals are continuous
time. We define a
discrete-time system
as one in which all signals are discrete time.
Both continuous-time and discrete-time signals appear in some physical systems; we
call these systems
hybrid systems,
or
sampled-data systems
. An example of a sampled-
data system is an automatic aircraft-landing system, in which the control functions
are implemented on a digital computer.
The mathematical analysis of physical systems can be represented as in
Figure 1.3 [1]. We first develop mathematical models of the physical systems and
signals involved. One procedure for finding the model of a physical system is to use
the laws of physics, as, for example, in (1.1). Once a model is developed, the equa-
tions are solved for typical excitation functions. This solution is compared with the
response of the physical system with the same excitation. If the two responses are
approximately equal, we can then use the model in analysis and design. If not,
we must improve the model.
Improving the mathematical model of a system usually involves making the
models more complex and is not a simple step. Several iterations of the process
illustrated in Figure 1.3 may be necessary before a model of adequate accuracy
results. For some simple systems, the modeling may be completed in hours; for very
complex systems, the modeling may take years. An example of a complex model is
that of NASA's shuttle; this model relates the position and attitude of the shuttle to
f(t)
f(t)
f(nT), n =Á, -2, -1, 0, 1, 2, Á ,
f(nT)
Problem formulation
Mathematical
models of systems
and signals
Physical
system
Conceptional
aspects
Mathematical
solution of
equations
Solution translation
FIGURE 1.3
Mathematical solutions of
physical problems.
