Biomedical Engineering Reference
In-Depth Information
8
7
6
5
4
3
2
1
0
t
0123456789
f
(
t
)
=
4
6
4
2
0
FIGURE 10.27
:
Graph B of the function,
f
(
t
)
=−
1
λ
+
8, with the interval
T
=
2. Note that
the values of the sampled function are 4, 6, 4, 2, and 0 at times
t
=
0, 2, 4, 6, and 8, respectively
2, which
then yields slightly different answers as shown by Fig. 10.27. Note that in Fig. 10.27,
the midpoints for the interval
T
However, one may elect to use the interval between
−
T
/
2
<
0
<
+
T
/
etc.
Let us convolve the
f
1
function with the values of the function
f
(
t
)
=
2areat
t
=
1
,
3
,
5
...
8,
as shown in Table 10.1 and Fig. (10.26). The calculations and results of the convolution
are given in Table 10.2 and are shown in Fig. (10.28). The results are labeled as A, since
the second function is composed of the values from Fig. 10.26.
=−
1
λ
+
TABLE 10.2:
Results A of Convolution with Fig. 10.26
t
=
1
2
3
4
5
6
f
1
=
0.5
1.5
2.5
3
3
3
f
2
=
7
5
3
1
0
3.5
10.5
17.5
21
21
21
2.5
7.5
12.5
15
15
15
1.5
4.5
7.5
9
9
9
0.5
1.5
2.5
3
2
1
0
0
0 000
Col Sum
3.5
13
26.5
38.5
45
47.5
27
11
1
0
f
1
×
f
2
=
(
)(
T
)
7
26
53
77
90
95
54
22
2
0
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