Biomedical Engineering Reference
In-Depth Information
f
( )
f
(
t
)
0
t
0
(a) Original function
(b) Change of variable
Ae
−
at
. (b) It shows the
FIGURE 10.17
:
First step. (a) It shows the original function
f
(
t
)
=
change of variable for the function
f
(- )
f
(- )
0
0
(a) Folding
(b) Translation
FIGURE 10.18
:
Next two steps. (a) It shows folding of the function about the
y
-axis and (b) it
shows the translation step
a.
Movement to the right for positive (
+
) time
b.
Movement to the left for negative (
−
) time
Let us visualize an example, in which two functions of unity magnitude are to be
convolved. Assume the two functions are given by (10.11) and (10.12).
f
1
(
t
)
=
1
μ
(
t
)
(10.11)
-
a
a
b
-
b
(
t
-
b
)
0
(
t
-
a
)
0
0
(a) Original
(b) Folded
(c) Translated
FIGURE 10.19
:
Another Example. It should be noted that the original does not begin at
t
0,
but is delayed by some magnitude
a
. Figures 10.19(a) through (c) show that the amount of delay
is carried through the Folding and Translation steps
=
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