NI Spectral Measurements Toolkit User Guide
28
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Averaged Power Spectrum
The following equations describe the averaging methods you can apply
to a complex FFT spectrum to yield an averaged power spectrum. The
No averaging method converts the complex FFT spectrum to a real power
spectrum.
The averaged power spectrum is equivalent to the square of the magnitude
of the averaged FFT spectrum.
Averaged Cross Spectrum
If you have two FFT spectra,
X
and
Y
, the cross spectrum
S
xy
results
from multiplying the complex conjugate of spectrum
X
by spectrum
Y
as
follows:
S
xy
= conj(
X
)
×
Y
For RMS averaging, an averaged cross spectrum consists of the average of
the individual cross spectra as follows:
S
xy
= < conj(
X
)
×
Y
>
For vector averaging, an averaged cross spectrum consists of the vector
average of each spectrum computed before multiplying the two averaged
spectra as follows:
S
xy
= conj(<
X
>)
×
<
Y
>
A cross spectrum has no peak-hold average.
Table 3.
Averaged Power Spectrum Averaging Methods and Equations
Averaging Method
Equation
No averaging
Y = X
conj(
X
)
Vector averaging
Y
k
= <
X
>
k
conj(<
X
>
k
)
RMS averaging
Y
k
= <
X
conj(
X
)>
k
Peak-hold
Y
k
= max(
X
k
,
Y
k-1
)
2
