App-12
IM 701830-01E
FFT function
Each frequency component G of a linear spectrum is represented by
G=R+jI (R: real part, I: imaginary part).
The dynamic ranges of the spectrums/functions are as follows.
Module 701855/701856 : 60 dB
Module 701852/701853 : 96 dB
Linear spectrum
Linear spectrum is a spectrum that can be directly determined with the FFT.
The magnitude and phase of each frequency component included in the measured waveform
can be found. Power spectrum and cross spectrum can also be determined from 1 or 2 linear
spectrums.
Since the FFT is a complex computation, real and imaginary parts can be obtained with the
linear spectrum. The magnitude and phase of the linear spectrum can also be determined from
the result.
The following spectrums can be determined with this instrument.
Item
Expression
Computation
Real
LS-REAL
R
Imaginary
LS-IMAG
I
Magnitude
LS-MAG
(R
2
+I
2
)
Log magnitude
LS-LOGMAG
20xlog
(R
2
+I
2
)
Phase
LS-PHASE
tan
-1
(I/R)
Reference log magnitude(0dB) : 1Vpeak
Rms value spectrum
Rms value spectrum expresses the rms value of the magnitude of the linear spectrum. It does
not contain phase information.
The following spectrums can be determined with this instrument.
Item
Expression
Computation
Magnitude
RS-MAG
(R
2
+I
2
)/2
Log magnitude
RS-LOGMAG
20xlog
(R
2
+I
2
)/2
Reference log magnitude(0dB) : 1Vrms
Power spectrum
Power spectrum expresses the power (squared value) of each frequency component included in
the measured signal. It is determined by taking the product of the linear spectrum and its
complex conjugate. It does not contain phase information.
The following spectrums can be determined with this instrument.
Item
Expression
Computation
Magnitude
PS-MAG
(R
2
+I
2
)/2
Log magnitude
PS-LOGMAG
10*log(R
2
+I
2
)/2
Reference log magnitude(0dB) : 1Vrms
2
Power spectrum density
Power spectrum density expresses the power spectrum per unit frequency. It is determined by
dividing the power spectrum with the frequency resolution
∆
f found during the analysis of the
power spectrum. The computation varies depending on the window function.
Power spectrum density is used to compare power spectrums analyzed at different frequency
bands. However, it is not necessary for signals having a line spectrum such as sine waves.
The following spectrums can be determined with this instrument.
Item
Expression
Computation
Magnitude
PSD-MAG
PS-MAG/
∆
f(For Rectangular window)
PS-MAG/1.5
∆
f(For Hanning window)
Log magnitude
PSD-LOGMAG 10xlogPS-MAG/
∆
f(For Rectangular window)
10xlogPS-MAG/1.5
∆
f(For Hanning window)
Reference log magnitude(0dB) : 1Vrms
2
Appendix 6 About User Defined Computations
