Hioki Memory HiCorder MR6000, Instruction Manual, Page: 383 / 392

377
FFT Definitions
The following figure presents an example of spectral analysis of a time-domain waveform multiplied
by a window function.
Multiplying the time-domain waveform by the window function eliminates discontinuous points on
the waveform, obtaining the spectrum with a lobe similar to the line spectrum.
Time-domain waveform Spectrum
0.1
0
−0.1
0.002 0.004 0.006 0.008 0.01 0
10 20 30 40 0
0
−200
−100
Time (s)
Amplitude (V)
Frequency (kHz)
Magnitude (dB)
Waveform obtained by multiplying the above-described waveform (“Time-domain
waveform when the number of analysis points is unequal to an integer multiple of the
input frequency” (p. 376)) by Blackman Harris window
The following figure illustrate the time-domain waveform multiplied by the window function and its
spectrum.
Each spectrum shows a highest peak at a low frequency, and many lower peaks at higher
frequencies. The highest peak is called the main lobe, and the smaller peaks are the side lobes.
A narrower width of the main lobe and lower lobes lead to accurate results of FFT analyses;
however, the conditions are incompatible with one another. Thus, if you wish to emphasize
altitudes, use a window function that has a wider main lobe. If you wish to observe spectra adjacent
to each other, use a window function that has a narrower main lobe. If you wish to eliminate the
effect of the adjacent spectra, use a window function that has smaller side lobe values.
Since the main lobe width is proportional to the width of the window (1/W), increasing the number
of analysis points increases the frequency resolution.
Rectangular window
Amplitude
0
0
1
N-1
G
ain (dB)
−20
−40
−60
0
Frequency (1/W)
−6 −4 −2 0 2 4 6
Time-domain waveform Spectrum
Hann (also referred to as Hanning) window
Amplitude
0
0
1
N-1
Gain (dB)
−20
−40
−60
0
Frequency (1/W)
−6 −4 −2 0 2 4 6
Time-domain waveform Spectrum
Appendix
HIOKI MR6000A966-03