Digital Signal Processing Reference
In-Depth Information
order and then command the A/D to sample. The receiving circuits separate out
the synchronizing information and switch the pulses, in order, to the correct digital-
to-analog converter.
In
pulse-width modulation,
the sampling process produces a rectangular pulse
of constant amplitude and variable width, with the pulse width proportional to the
signal amplitude. In
delta modulation,
the output of the sampling process is the dif-
ference in the present sample and the previous sample. All four sampling processes
are used in telephone communications.
Data-acquisition systems
are instrumentation systems in which the taking of mea-
surements is controlled automatically by a computer. A typical system is illustrated
in Figure 1.25. In this figure, we have assumed that measurements from
n
different
sensors are to be recorded in computer memory. The computer controls the multi-
plexer and, hence, determines which measurement is recorded at a given time. In
some large data-acquisition systems, the number of sensors is greater than 1000.
When switching occurs in the input multiplexer in Figure 1.25, the transient
circuit is often modeled as in Figure 1.26(a). The sensor is modeled as a Thévenin
equivalent circuit [9], with (constant) source voltage and source resistance
The voltage is the voltage internal to the analog-to-digital converter that is
converted to a binary number. (See Figure 1.19.) Resistance is the equivalent re-
sistance of the circuit from the input terminals to the voltage and repre-
sents the stray capacitance in the circuit. Generally, the resistance of the remainder
of the circuit at the voltage is sufficiently large that it can be ignored.
The voltage exponentially approaches the constant value of the sen-
sor, as shown in Figure 1.26(b). The initial value of (that value at the instant of
switching) is, in general, unknown; a value is given in Figure 1.26(b). The transient
term in is of the form with
V
constant and the time constant
(Time constants are discussed in Section 2.3.) Theoretically, this
term never goes to zero and the system never reaches steady state. We see then that
V
s
R
s
.
v
ad
(t)
R
a
v
ad
(t),
C
a
v
ad
(t)
v
ad
(t)
V
s
v
ad
(t)
Ve
-t/t
,
v
ad
(t)
t = (R
s
+ R
a
)C
a
.
Sensors
Multiplexer
1
2
A/D
Computer
n
Control
signals
Figure 1.25
Data-acquisition system.
