Digital Signal Processing Reference
In-Depth Information
TABLE 9.2
Values for Example 9.2
mx
[
m
]
n
=
2
-
m
y
[
n
]
-1
2
3
2
0
1
2
1
1
0
1
0
2
2
0
2
Table 9.2 gives values of
n
for significant values of
m
. Because only four points are involved,
y
[
n
] is also included in this table. In Figure 9.11(a), the
n
-axis is shown directly below the
m
-
axis. The
n
-axis values are given in the third column of Table 9.2.
Next we plot versus
n
to show the transformed signal. This plot can be
made directly from Figure 9.11(a) or from Table 9.2, and is shown in Figure 9.11(b).
y[n] = x[2 - n]
■
Example 9.2 illustrates two procedures for plotted time-transformed signals.
We can draw the
n
-axis below the plot of the signal, as in Figure 9.11(a), or we can
construct a table like Table 9.2.
Next we consider the three transformations on the amplitude axis. Amplitude trans-
formations follow the same rules as time transformations.
The three transformations in amplitude are of the general form
y[n] = Ax[n] + B,
(9.24)
where
A
and
B
are constants that are not necessarily integers; for example,
y[n] =-3.1x[n] - 5.75.
The value yields
amplitude reversal
(the minus sign) and
amplitude scal-
ing
and the value gives
amplitude shifting
and changes the
dc level (the average value) of the signal. An example of amplitude scaling is now
given.
A =-3.1
(
ƒ
A
ƒ
= 3.1),
B =-5.75
Amplitude transformations of a discrete signal
EXAMPLE 9.3
Consider again the signal of Example 9.2 and Figure 9.11(a). This signal is repeated in
Figure 9.12(a). We will plot the transformed signal
y[n] = 3 - 2x[n].
