Hioki MR8740-50, Инструкция по эксплуатации

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170
Operators of Waveform Calculation and Calculation Results
b
i
:
i
th data point of calculation results,
d
i
:
i
th data point acquired across the source channel
Waveform calculation
type
Description
Arc sine (ASIN)
With d
i
> 1 b
i
= π / 2
With
−1 ≤ d
i
≤ 1 b
i
= arcsin( d
i
)
With d
i
< −1 b
i
= −π / 2 ( i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Arc cosine (ACOS)
With d
i
> 1 b
i
= 0
With
−1 ≤ d
i
≤ 1 b
i
= arccos( d
i
)
With d
i
< −1 b
i
= π ( i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Arc tangent (ATAN)
b
i
= arctan( d
i
) ( i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Arc tangent 2
(ATAN2(y, x))
Responses arc tangent of (
y / x
) in the range of [ −π , π ]. Specify numbers in radians (rad).
ATAN2( y , x ) =
With
x
≥ 0 ATAN(
y
/
x
)
With x < 0 and y ≥ 0 ATAN( y / x ) + π
With
x
< 0 and
y
< 0 ATAN(
y
/
x
) − π
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
1
.
Note If the instrument differentiates a waveform that oscillates slowly, calculation results
vary significantly.
In such a case, raise the second parameter of the function.
The following expressions hold provided 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
through b
n
: Calculation result data
h
= Δ
t
: Sampling interval
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