Hioki Memory HiCorder MR6000, Instruction Manual, Page: 209 / 392

203
Operators of the Waveform Calculation and Calculation Results
b
i
:
i
th-point data in calculation results,
d
i
:
i
th-point data acquired across the source channel
Waveform calculation
type
Description
1st-order differential
(DIF)
2nd-order differential
(DIF2)
The instrument makes 1st-order differential and 2nd-order differential calculations using
5th-order Lagrange interpolation formula to obtain 1-point data from 5-point values that
includes before and after the point.
The instrument differentiates data d
1
to d
n
considering them as the corresponding data
for the sampling time
t
1
to
t
n
.
Note: Differentiating a slowly oscillating waveform causes an increase in calculation
results variation.
In such a case, raise the second parameter of the function.
The following equations hold when the second parameter equals one.
Arithmetic expressions of 1st-order differential
Point
t
1
b
1
= (−25
d
1
+ 48
d
2
− 36
d
3
+ 16
d
4
− 3
d
5
) / 12
h
Point
t
2
b
2
= (−3 d
1
− 10 d
2
+ 18 d
3
− 6 d
4
+ d
5
) / 12 h
Point
t
3
b
3
= (
d
1
− 8
d
2
+ 8
d
4
−
d
5
) / 12
h
↓
Point
t
i
b
i
= (
d
i −2
− 8
d
i −1
+ 8
d
i +1
−
d
i +2
) / 12
h
↓
Point
t
n-2
b
n-2
= (
d
n-4
− 8
d
n-3
+ 8
d
n-1
−
d
n
) / 12
h
Point
t
n-1
b
n-1
= (− d
n-4
+ 6 d
n-3
− 18 d
n-2
+ 10 d
n-1
+ 3 d
n
) / 12 h
Point
t
n
b
n
= (3
d
n-4
− 16
d
n-3
+ 36
d
n-2
− 48
d
n-1
+ 25
d
n
) / 12
h
b
1
to b
n
: Calculation result data
h
= Δ
t
: Sampling period
Arithmetic expressions of 2nd-order differential
Point t
1
b
1
= (35 d
1
− 104 d
2
+ 114 d
3
− 56 d
4
+ 11 d
5
) / 12 h
2
Point
t
2
b
2
= (11 d
1
− 20 d
2
+ 6 d
3
+ 4 d
4
− d
5
) / 12 h 2
Point t
3
b
3
= (− d
1
+ 16 d
2
− 30 d
3
+ 16 d
4
− d
5
) / 12 h
2
↓
Point t
i
b
i
= (− d
i −2
+ 16 d
i −1
− 30 d
i
+ 16 d
i +1
− d
i +2
) / 12 h
2
↓
Point t
n-2
b
n-2
= (− d
n-4
+ 16 d
n-3
− 30 d
n-2
+ 16 d
n-1
− d
n
) / 12 h
2
Point
t
n-1
b
n-1
= (− d
n-4
+ 4 d
n-3
+ 6 d
n-2
− 20 d
n-1
+ 11 d
n
) / 12 h 2
Point t
n
b
n
= (11 d
n-4
− 56 d
n-3
+ 114 d
n-2
− 104 d
n-1
+ 35 d
n
) / 12 h
2
W
aveform Calculation Function
HIOKI MR6000A966-03