Digital Signal Processing Reference
In-Depth Information
Sensor
Inverse
of
thermistor
Temperature
Tempe
r
ature
Thermistor
Figure 2.40
Temperature sensor.
Resistance
The discussion in the preceding paragraph applies to transducers in general. In
measuring physical variables (signals), we measure the
effect
of the physical variable
on the transducer. We must be able to determine the input to the transducer (the
physical variable) by measuring the transducer's output (the effect of the physical
variable). This cause-and-effect relationship must be invertible. A
sensor
is a trans-
ducer followed by its inverse system and is illustrated in Figure 2.40.
A glass-bulb thermometer is a second example of a transducer. The glass bulb is the
system, and the scale attached to the bulb is the inverse system. A change in tempera-
ture causes a change in the density of the liquid in the bulb. As a result, the level in the
column of liquid changes. The calibrated scale then converts the liquid level to units of
temperature.
The output signal of the inverse system seldom has the same units as the sys-
tem input signal; however, the amplitudes of the two signals are equal.
Causality
A system is causal if the output at any time
t
0
is dependent on the input only for
t … t
0
.
A causal system is also called a
nonanticipatory system. All physical systems are
causal
.
A
filter
is a physical device (system) for removing certain unwanted components from
a signal. We can design better filters for a signal if all past values and all future values
of the signal are available. In real time (as the signal occurs in the physical system), we
never know the future values of a signal. However, if we record a signal and then filter
it, the “future” values of the signal are available. Thus, we can design better filters if
the filters are to operate only on recorded signals; of course, the filtering is not per-
formed in real time.
A system described by
y(t) = x(t - 2),
(2.67)
with
t
in seconds, is causal, since the present output is equal to the input of 2 s ago.
For example, we can realize this system by recording the signal
x
(
t
) on magnetic
tape. The playback head is then placed 2 s downstream on the tape from the record-
ing head. A system described by (2.67) is called an
ideal time delay
. The form of the
signal is not altered; the signal is simply delayed.
A system described by
y(t) = x(t + 2)
(2.68)
