Tektronix AWG2021 User Manual page 195

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3 76
Y
3
Y
2
Y '
2
Y
1
X X ' X
1 2
Figure 3 56: Quadratic Interpolation
Quadratic interpolation is expressed as follows.
f ( x ) + Ax ) Bx ) C
2
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.
+ Ax ) Bx
2
y
1 1
1
+ Ax ) Bx
2
y
2 2
2
+ Ax ) Bx
2
y
3 3
3
Simplifying by letting x
+ A * B ) C
y
1
+ C
y
2
+ A ) B ) C
y
3
This allows the coefficients A, B, and C to be derived as follows:
) y
y
A + * y
1 3
2
* y
y
B +
3 1
2
C + y
2
Using these values, the value y
) y
y
+ ( * y
1 3
y
2
2
X
2 3
) C
) C
) C
= –1, x = 0, x = 1, gives:
1 2 3
2
' at position x
2
* y
y
) (
3 1
2
) (* 0.2)
2
2
' can be derived as follows.
2
(* 0.2) ) y
)
2
AWG2021 User Manual