EDIT Menu

Y3

Y2

Y2'

Y1

X1

X2' X2

X3

Figure 3 ￿56: Quadratic Interpolation

Quadratic interpolation is expressed as follows.

f (x) + Ax2 ) 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.

y1 + Ax21 ) Bx1 ) C

y2 + Ax22 ) Bx2 ) C

y3 + Ax23 ) Bx3 ) C

Simplifying by letting x1 = ±1, x2 = 0, x3 = 1, gives:

y1 + A * B ) C y2 + C

y3 + A ) B ) C

This allows the coefficients A, B, and C to be derived as follows:

A +

y1

) y3

* y2

 

2

 

 

 

B +

y3

* y1

 

 

2

 

 

 

 

C + y2

Using these values, the value y2 ' at position x2 ' can be derived as follows.

y2￿ + (

y1 ) y3

* y2)

(* 0.2)

2 ) (

y3 * y1

) (* 0.2) ) y2

 

 

2

 

 

2

 

3 ￿76

AWG2021 User Manual