Biomedical Engineering Reference
In-Depth Information
TABLE 10.1:
Convolution by Multiplication Method
t
=
1
2
3
4
5
6
f
1
=
0.5
1.5
2.5
3
3
3
f
2
=
9.5
8.5
7.5
6.5
5.5
at
n
=
19
.
5
×
f
1
(
n
=
1
..
6)
4.75
14.25
23.75
28.5
28.5
28.5
at
n
=
18
.
5
×
f
1
(
n
=
1
..
6)
4.25
12.75
21.25
24.5
24.5
24.5
at
n
=
17
.
5
×
f
1
(
n
=
1
..
6)
3.75
11.3
. . .
. . .
. . .
at
n
=
16
.
5
×
f
1
(
n
=
1
..
6)
3.25
. . .
. . .
. . .
at
n
=
15
.
5
×
f
1
(
n
=
1
..
6)
2.75
. . .
. . .
f
1
×
f
2
=
(
×
T
)
4.75
18.5
40.25
64.3
. . .
. . .
. . .
calculations. The question arises as to where to take the values from the time varying
function within a fixed interval. Specifically, the question may be rephrased as “Where
should the interval be located?” For example, a function,
f
(
t
)
=−
1
λ
+
8, can be sam-
pled with some interval of time,
T
, in the following manner: Let
T
2 and the value
be selected at midinterval, as in Fig. 10.26. The general procedure is to take the average
value of the function
f
(
t
) in the interval,
kT
, where
k
is the sample number.
=
8
7
6
5
4
3
2
1
0
t
0 12345678
f
(
t
)
=
7
5
3
1
FIGURE 10.26
:
Graph A of the function,
f
(
t
)
=−
1
λ
+
8, with the interval
T
=
2. Note that
the values of the sampled function are 7, 5, 3, and 1 at times
t
=
1, 3, 5 and 7, respectively
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