Hioki 8847 - 13.3 Setting FFT Analysis Conditions

11.3 Waveform Calculation Operators and Results
199
11
Chapter 11 Waveform Calculation Functions
Arccosine (ACOS)
When d
i
> 1, b
i
= 0
When -1
≤ d
i
≤ 1, b
i
= acos(d
i
)
When d
i
< -1 , b
i
= π (i = 1, 2, .... n)
Trigonometric functions employ radian (rad) units.
Arctangent (ATAN)
b
i
= atan(d
i
) (i = 1, 2, .... n)
Trigonometric functions employ radian (rad) units.
First derivative (DIF)
Second derivative (DIF2)
The first and second derivative calculations use a fifth-order Lagrange interpolation poly-
nomial to obtain a point data value from five sequential points.
d
1
to d
n
are the derivatives calculated for sample times t
1
to t
n
.
Note: Scattering of calculation results increases as input voltage level decreases. If scat-
tering is excessive, apply the moving average (MOV).
Calculation formulas for the first derivative
Point t
1
b
1
= (-25d
1
+ 48d
2
- 36d
3
+ 16d
4
- 3d
5
)/ 12h
Point t
2
b
2
= (-3d
1
- 10d
2
+ 18d
3
- 6d
4
+ d
5
)/ 12h
Point t
3
b
3
= (d
1
- 8d
2
+ 8d
4
- d
5
)/ 12h
↓
Point t
i
b
i
= (d
i -2
- 8d
i-1
+ 8d
i+1
- d
i+2
)/ 12h
↓
Point t
n-2
b
n-2
= (d
n-4
- 8d
n-3
+ 8d
n-1
-d
n
)/12h
Point t
n-1
b
n-1
= (-d
n-4
+ 6d
n-3
- 18d
n-2
+ 10d
n-1
+ 3d
n
)/12h
Point t
n
b
n
= (3d
n-4
- 16d
n-3
+ 36d
n-2
- 48d
n-1
+ 25d
n
)/12h
b
1
to b
n
: calculation results
h =
Δt : Sampling Period
Calculation formulas for the second derivative
Point t
1
b
1
= (35d
1
- 104d
2
+ 114d
3
- 56d
4
+ 11d
5
)/12h
2
Point t
2
b
2
= (11d
1
- 20d
2
+ 6d
3
+ 4d
4
- d
5
)/12h
2
Point t
3
b
3
= (-d
1
+ 16d
2
-30d
3
+ 16d
4
- d
5
)/12h
2
↓
Point t
i
b
i
= (-d
i-2
+ 16d
i-1
- 30d
i
+ 16d
i+1
- d
i+2
)/12h
2
↓
Point t
n-2
b
n-2
= (-d
n-4
+ 16d
n-3
- 30d
n-2
+ 16d
n-1
- d
n
)/12h
2
Point t
n-1
b
n-1
= (-d
n-4
+ 4d
n-3
+ 6d
n-2
- 20d
n-1
+ 11d
n
)/12h
2
Point t
n
b
n
= (11d
n-4
-56d
n-3
+ 114d
n-2
- 104d
n-1
+ 35d
n
)/12h
2
b
i
: ith member of calculation result data, d
i
: ith member of source channel data
Waveform Calculation Type Description