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3 Ć76
AWG2021 User Manual
Y3
Y2
Y2'
Y
1
X1 X2'X2 X3
Figure 3 Ć56: Quadratic Interpolation
Quadratic interpolation is expressed as follows.
f
(
x
)
+ Ax
2
) Bx ) C
The coefficients A, B, and C in the above formula are derived using the three
points including those directly preceding and following the position to be
derived.
y
1
+ Ax
2
1
) Bx
1
) C
y
2
+ Ax
2
2
) Bx
2
) C
y
3
+ Ax
2
3
) Bx
3
) C
Simplifying by letting x
1
= –1, x
2
= 0, x
3
= 1, gives:
y
1
+ A * B ) C
y
2
+ C
y
3
+ A ) B ) C
This allows the coefficients A, B, and C to be derived as follows:
A +
y
1
) y
3
2
* y
2
B +
y
3
* y
1
2
C + y
2
Using these values, the value y
2
’ at position x
2
’ can be derived as follows.
y
Ȁ
2
+ (
y
1
) y
3
2
* y
2
) (* 0.2)
2
) (
y
3
* y
1
2
) (* 0.2) ) y
2