Digital Signal Processing Reference
In-Depth Information
Amplitude
f
(
t
)
f
(
nT
)
2
T
T
T
2
T
3
Tt
0
(a)
Timing signal
from computer
f
(
t
)
f
(
nT
)
Analog-to-digital
converter
Data to
computer
(b)
A/D
Computer
f
(
t
)
f
[
n
]
g
[
n
]
Digital
processor
Sampler
f
(
nT
)
Figure 9.1
Hardware diagram for sampling
and processing.
(c)
not
universal; it is used here in an attempt to differentiate between
f(nT)
and
f[n].
If
f[n]
is obtained from
f(t)
by sampling every
T
seconds, then
f(nT) = f(t) ƒ
t =nT
and
f[n] = f(t) ƒ
t =nT
Z f(t) ƒ
t =n
.
(9.1)
Figure 9.1(c) illustrates a total system for digital signal processing. The sampler con-
verts the continuous-time signal into the discrete-time signal the
output of the processor is the signal
g
[
n
]. While is defined for all time,
g
[
n
] is
defined only for
n
an integer; for example,
g
[1.2] simply does not exist.
A discrete-time signal
x
[
n
] can be a
continuous-amplitude signal,
for which
the amplitude can assume any value A second class of discrete-
time signals is a
discrete-amplitude signal,
for which
x
[
n
] can assume only certain
defined amplitudes. A discrete-amplitude discrete-time signal is also called a
digital
signal
.
An example of a discrete-amplitude discrete-time signal is the output of an
analog-to-digital converter. (See Figure 1.19.) For example, if the binary signal out
of an analog-to-digital converter is represented by eight bits, the output-signal am-
plitude can assume only different values. A second example of a discrete-
amplitude discrete-time signal is any signal internal to a digital computer.
f(t)
f(nT) = f[n];
f(t)
-
q
6 x[n] 6
q
.
2
8
= 256
