Hioki Memory HiCorder MR6000, Instruction Manual, Page: 381 / 392

375
FFT Definitions
Averaging
With the FFT function, averaging used the following expressions.
(1) Simple average
Add acquired data sets in series and divides the sum by a acquisition count.
𝐴𝐴
𝑛𝑛
=
(𝑛𝑛 − 1)𝐴𝐴
𝑛𝑛−1
+ 𝑍𝑍
𝑛𝑛
𝑛𝑛
...............................................................(11)
n : Acquisition count for averaging
A
n
:
n
th averaging result
Z
n
: n th waveform data set
(2) Exponential average
Calculates an weighted average such that newer data points contribute more than others.
𝐴𝐴
𝑛𝑛
=
(𝑁𝑁 − 1)𝐴𝐴
𝑛𝑛−1
+ 𝑍𝑍
𝑛𝑛
𝑁𝑁
..............................................................(12)
N : Specified number of acquisition for averaging
n
: Acquisition count for averaging (
n
≥ 2)
A
n
: n th averaging result ( A
1
= Z
1
)
Z
n
:
n
th waveform data set
Overall value
The overall value shows the sum of power spectra of each frequency. This value is nearly equal to
the sum of the squares of an input signal (square of RMS value)(except when frequency averaging
is performed). With the FFT function, the instrument displays RMS values for stored waveforms,
or overall values for frequency-domain waveforms calculated using the sum of power spectra. Any
FFT analysis modes other than the power spectrum, however, take the root square of the overall
value to match the unit.
With the FFT analysis mode set to the power spectrum
....................................................................(13-1)
With the FFT analysis mode set to the histogram, linear spectrum, RMS spectrum, impulse response, 1/1
octave analysis, or 1/3 octave analysis
..............................................................(13-2)
P
i
:
i
th power spectrum
Total harmonic distortion factor (THD)
The total harmonic distortion factor (THD) indicates a percentage of the total harmonic to the
fundamental.
The more severely the waveform distorts, the larger the value becomes.
THD =
( )
( )
×
∑
V
V
n
2
0
100
[%] ........................................................(14)
V
0
: Fundamental wave
V
n
:
n
th order harmonic
Appendix
HIOKI MR6000A966-03