FFT Mode
4-7
•P.S.D. (Power Spectrum Density)
The "Power Spectrum Density" refers to the power spectrum per unit frequency.
The result of FFT analysis is an integral value of the power spectrum that is
distributed along a bandwidth (the width of the frequency resolution) that is
determined by the selected frequency for FFT analysis (the Frequency setting)
and the selected number of points to be analyzed (the Counts setting). When the
signals of a power spectrum form a continuous spectrum, therefore, the resulting
value varies with the currently selected Frequency and Counts settings. In the
case of signals of a spectrum that is distributed along a wide bandwidth, using a
Function setting of P.S.D. will allow you to obtain measured values that are
unrelated to the Frequency and Counts settings.
10 log
FFT result of measured signals : X(i) = XR(i) + jX I (i)
∆f: Analysis band width
[V
rms
2
]
S
R
(i)
2
+ S
I
(i)
2
2
[V
2
/Hz]
X
R
(i)
2
+ X
I
(i)
2
∆f
[dBVrms/Hz]
X
R
(i)
2
+ X
I
(i)
2
2∆f
10 log [dBV/Hz]
X
R
(i)
2
+ X
I
(i)
2
∆f
tan
—1
[deg]
X
I
(i)
X
R
(i)
∆f[Hz]
Frequency setting
Counts setting 0.4
Display
RMS = Off RMS = On
Y axis
Amplitude
LIN.
LOG.
PhasePhase
– The amplitude is the voltage of the reference wave height value.
–When the RMS setting is On, the root-mean-square value is displayed instead.
– When the Y (axis) setting is LOG., the reference value is either 0 dB/Hz = 1 V2/
Hz or 0 dBVrms/Hz = 1Vrms2/Hz.
–When the Y (axis) setting is Phase, the Phase display is identical to that for the
Linear Spectrum setting shown in the preceding table.
• Cross (Cross Spectrum)
This cross spectrum is the product of the spectrum of two signals for a specific
frequency component. It indicates the correlation and relative power of both
signals. When the Function setting is Cross, the cross spectrum of the signal input
and signal output is measured and averaged. Compared with only measuring the
power spectrum of the signal output, therefore, you can substantially lower the
impact of noise, even for a system in which noise mixes into the signal input.
10 log
FFT result of measured signals : X(i) = X
R
(i) + jX
I
(i)
Y(i) = Y
R
(i) + jY
I
(i)
S
R
(i) = X
R
(i)Y
R
(i) + X
I
(i)Y
I
(i)
S
I
(i) = X
R
(i)Y
I
(i) - XI(i)Y
R
(i)
[V
rms
2
]
S
R
(i)
2
+ S
I
(i)
2
2
[dBV
rms
]
S
R
(i)
2
+ S
I
(i)
2
2
10 logS
R
(i)
2
+ S
I
(i)
2
[dBV]
tan
—1
[deg]
X
I
(i)
X
R
(i)
S
R
(i)
2
+ S
I
(i)
2
[V
2
]
Display
RMS = Off RMS = On
Y axis
Amplitude
LIN.
LOG.
PhasePhase
– The amplitude is the voltage of the reference wave height value.
–When the RMS setting is On, the root-mean-square value is displayed instead.
–When the Y (axis) setting is LOG., the reference value is either 0 dB = 1 V2 or 0
dBVrms = 1 Vrms
2
.
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