Hioki MR8740, Instruction Manual

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Appendix 4 FFT Definitions
A
21
Appe
ndix
The following figure presents an example of spectral analysis by applying a win-
dow function to a time-domain waveform.
Using the window function, discontinuous points on the time-domain waveform
are eliminated, so the wave shape approaches a line spectrum.
The following figure shows the time-domain waveform of the window function
and its spectrum.
Each spectrum shows a large peak at a low frequency, and many smaller peaks
at higher frequencies. The largest peak is called the
main lobe , and the smaller
peaks are the side lobes .
The most accurate results of the FFT function are obtained when the width of the
main lobe and the amplitude of the side lobes are minimized, although both con-
ditions cannot be satisfied at the same time.
Therefore, a window function having a wide main lobe is used when amplitude
values are important, while a window function having a small main lobe is used
to observe fine spectral details, and a window function having small side lobe
amplitudes is used to exclude the effects of the surrounding spectrum.
However, because the main lobe width is proportional to the width (1/W) of the
window, increasing the number of analysis points increases the frequency reso-
lution.
0 0.002 0.004 0.006 0.008 0.01
-0.1
0
0.1
Time [sec]
Amplitude
[V]
When a Blackman-Harris window function is applied to a time-domain
waveform (
⇒
p.20) in which the number of analysis points is not an inte-
ger multiple of the input frequency
Spectrum
0 10 20 30 40
-200
-100
0
Frequency [kHz]
Ma
gn
itu
de
[d
B]
Time-Domain Waveform
Rectangular window
Time-Domain Waveform Spectrum
Hann window
Time-Domain Waveform Spectrum
N-1 0
Ampli
tude
0
0 2 4 6 8 10
-80
-60
-40
-20
0
Frequency (1/W)
Gain
[
dB]
N-1 0
A
m
pl
it
ude
0
0 2 4 6 8 10
-80
-60
-40
-20
0
Frequency ( 1/W)
Ga
in [
dB]