Digital Signal Processing Reference
In-Depth Information
dy
(
t
)
dt
x
(
t
)
y
(
t
)
2
y
(
t
)
2
(a)
x
(
t
)
y
(
t
)
1
s
2
(b)
Figure 3.25
System for Example 3.19.
■
In Example 3.19, a block diagram for a differential equation, based on an inte-
grator, was constructed for a first-order differential equation. Figure 3.25(a) shows
the three components used in constructing block diagrams of this type:
1.
integrators
2.
summing devices (the circle)
3.
gains (the block with a gain of
-2
)
Figure 3.25(a) is also useful in realizing analog filters. If the result of an analog-
filter design is the transfer function we can implement the filter
as a physical device by using an integrator and amplifiers (including summing
amplifiers), as shown in Figure 3.25(a).
An
analog computer
is an electronic device that is used to solve differential
equations by the interconnection of electronics circuits that (1) integrate signals,
(2) sum signals, and (3) amplify (or attenuate) signals. The system of Fig-
ure 3.25(a) can be programmed directly on an analog computer, and the result will
be the solution of the system differential equation for an applied voltage input
function A
simulation
is a machine solution of the equations that model a
system. The analog computer is used for
analog simulations
of continuous-time
systems.
If the integrator of Figure 3.25(a) is replaced with a numerical integrator,
the resulting equations can be programmed on a digital computer, yielding a nu-
merical solution of the differential equation. In this case, we have a machine solu-
tion, called a
digital simulation,
of the differential-equation model. For these
reasons, block diagrams of the type given in Figure 3.25(a) are sometimes called
simulation diagrams
. One procedure for constructing either an analog simulation
or a digital simulation of a system is, first, to draw a simulation diagram that is
based on integrators.
H(s) = 1/(s + 2),
x(t).
