Digital Signal Processing Reference
In-Depth Information
Digital-
to-analog
converter
Power
amplifier
x
[
n
]
x
v
(
t
)
D/A
K
From
computer
Speaker
(a)
x
[
n
]
x
v
(
t
)
n
t
0
T
2
T
01 2
(b)
(c)
Figure 9.16
Computer generation of a tone.
Ideal time
delay
x
[
n
]
x
[
n
1
]
D
Ideal time
delay
ax
[
n
1]
a
x
[
n
]
x
[
n
1
]
D
Multiplication
(a)
(b)
Figure 9.17
Discrete-time system.
Suppose that at the first instant (denoted as
n = 0
), the number unity is stored in
the delay; that is,
x[0] = 1.
We now iteratively solve for
x[n], n 7 0,
using (9.44)
(recall that the ideal time delay outputs its number every
T
seconds):
x[1] = ax[0] = a
;
x[2] = ax[1] = a
2
;
x[3] = ax[2] = a
3
;
o ;
x[n] = ax[n - 1] = a
n
.
x[n] = a
n
Thus, this system generates the signal
for the initial condition x[0] = 1.
