Biomedical Engineering Reference
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Autocorrelation direct translation
2
1.5
1
f
1
0.5
S1
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Time (
t
)
FIGURE 9.2
:
Step 2: Translation. Negative translation of function along the
x
-axis
9.4 NUMERICAL CORRELATION: DIRECT
CALCULATION
9.4.1 Strips of Paper Method
One of the numerical methods is to use two strips of paper in the following steps:
1.
Tabulate values of the function at equally spaced intervals on two strips of
paper
2.
Reverse tabulate one function;
f
(
−
λ
), which is equivalent to folding a function
Autocorrelation 2 Positive Shift of
f
2
1.5
1
f
1
f
1
0.5
0
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Time (
t
)
FIGURE 9.3
:
Positive translation. The second function is moved in a positive direction by 2
delays along the
x
-axis. Note the overlapping area of both functions between 0 and
+
2 on the
x
-axis
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