Appendix 5 FFT Definitions
A
21
Appendi
x
Averaging_____________________________________________________
With the FFT function, averaging is performed according to the following analyti-
cal expressions. Averaging in the time domain produces meaningless data if per-
formed with inconsistent trigger criteria.
1. Simple Averaging (Time and Frequency Domains)
Sequences of acquired data are summed and divided by the number of acquisi-
tions.
n:
count of measurements to average
A
n
:
averaging results of
n
counts
Z
n
:
measurement data of
n
counts
2. Exponential Averaging (Time and Frequency Domains)
Before averaging, newer data is given exponentially greater significance than
older data.
N:
Specified number of counts to average
n:
count of measurements to average
A
n
:
averaging results of
n
counts
Z
n
:
measurement data of
n
counts
Overall Value __________________________________________________
The overall value is the sum of the power spectrum at each frequency. This
value is equal to the positive sum of the squares of the (RMS) input signals,
except when frequency averaging is performed. The FFT function of this instru-
ment calculates and displays the RMS values for stored waveforms and the
overall value from the sum of the power spectrum for the frequency domain.
P
i
:
power spectrum of value
i
Total harmonic distortion (THD) __________________________________
Total harmonic distortion (THD) indicates the proportion of the higher harmonics
to the fundamental harmonic
This means that the larger the value, the more distorted the waveform.
(11)
n
Z
A
n
A
n
n
n
+
−
=
−
1
)
1
(
(12)
N
Z
A
N
A
n
n
n
+
−
=
−
1
)
1
(
(13)
=
=
0
)
(
i
i
P
all
Over
THD
Σ
f
n
( )
2
f
0
( )
2
---------------
100
×
=
f
0
= fundamental wave
f
n
=
n
next higher harmonic
[%]
Summary of Contents for 8847
Page 1: ...MEMORY HiCORDER Instruction Manual 8847 December 2010 Revised edition 4 8847A981 04 10 12H ...
Page 2: ......
Page 18: ...Operating Precautions 8 ...
Page 26: ...1 4 Basic Key Operations 16 ...
Page 74: ...4 4 Waveform Observation 64 ...
Page 98: ...5 5 Managing Files 88 ...
Page 110: ...6 6 Miscellaneous Printing Functions 100 ...
Page 126: ...7 8 Seeing Block Waveforms 116 ...
Page 160: ...8 10 Making Detailed Settings for Input Modules 150 ...
Page 198: ...10 6 Numerical Calculation Type and Description 188 ...
Page 296: ...15 7 Controlling the Instrument with Command Communications LAN USB 286 ...
Page 304: ...16 2 External I O 294 ...
Page 362: ...Appendix 5 FFT Definitions A28 ...
Page 368: ...Index Index 6 ...
Page 369: ......
Page 370: ......
Page 371: ......