YOKOGAWA DL7440 User Manual

App-23
IM 701450-01E
App
Appendix
FFT Function
Each frequency component G of a linear spectrum is represented by
G=R+jI (R: real part, I: imaginary part).
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. The power spectrum and cross spectrum can also be determined from
one or two linear spectrums. Because the FFT is a complex function, the linear
spectrum produces the real part and imaginary part of the frequency components. 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 Equation Computation
Real part LS-REAL R
Imaginary part LS-IMAG I
Amplitude LS-MAG
(R
2
+ I
2
)
Log magnitude LS-LOGMAG 20×log
(R
2
+ I
2
)
Phase LS-PHASE tan
–1
(I/R)
Log magnitude reference (0 dB): 1 Vpeak
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 Equation Computation
Amplitude PS-MAG DC component R
2
+I
2
AC component (R
2
+I
2
)/2
Log magnitude PS-LOGMAG DC component 10×log(R
2
+I
2
)
AC component 10×log{(R
2
+I
2
)/2}
Log magnitude reference (0 dB): 1 Vrms
2
Power Spectrum Density
Power spectrum density expresses the power spectrum per unit frequency. It is
determined by dividing the power spectrum by 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 Equation Computation
Amplitude PSD-MAG PS-MAG/∆f (for rectangular window)
PS-MAG/1.5∆f (for Hanning window)
Log magnitude PSD-LOGMAG 10×logPS-MAG/∆f (for rectangular window)
10×logPS-MAG/1.5∆f (for Hanning window)
Log magnitude reference (0 dB): 1 Vrms
2
Appendix 4 User-Defined Computation

YOKOGAWA DL7440 Specifications

General

Brand	YOKOGAWA
Model	DL7440
Category	Test Equipment
Language	English