Amplitude, Power, Power spectral density – Campbell Scientific CR9000X Measurement and Control System User Manual
Page 278: Rms amplitude
Section 7. Measurement Instructions
7-54
Amplitude
The amplitude and phase option returns the amplitude as described above, plus
the phase in radians given by:
⎟
⎠
⎞
⎜
⎝
⎛
−
r
i
1
tan
.
The FFT calculation produces FFTLen/2 +1 pairs of amplitude and phase
components. ILow and IHigh, described below, determine which of these
pairs of values are returned by FFTFilt. The phase is between -
π and π.
Power
The power spectrum option gives the power for each of the spectral
components. The FFT calculation produces FFTLen/2 +1 power components.
ILow and IHigh, described below, determine the number of values returned by
FFTFilt. The CR9052DC computes the power from:
(
)
2
2
2
2
N
i
r
+
for all spectral components except the dc and Nyquist components. The dc
component is computed from
(
)
2
2
2
N
i
r
+
,
and the Nyquist component is computed from
(
)
2
2
2
2N
i
r
+
.
The sum of all of the ac components of the power spectrum gives the variance
of the original time series. The units of the power spectrum are
( )
2
mV
.
Power
Spectral
Density
The power spectral density (PSD) function normalizes the power spectrum by
the bandwidth of each spectral component. The FFT calculation produces
FFTLen/2 +1 PSD components. ILow and IHigh, described below, determine
the number of values returned by FFTFilt. The CR9052DC computes the psd
from:
(
)
SR
f
N
i
r
2
2
2
+
for all components except the dc and Nyquist components.
f
SR
is the sample
rate of the original time series (FSampRate). The dc component is computed
from:
(
)
SR
f
N
i
r
2
2
+
,
and the Nyquist component is computed from:
(
)
SR
f
N
i
r
2
2
2
+
.
The integral of the PSD over all of the ac components gives the variance of the
original time series. The units of the PSD are
( )
Hz
mV
2
.
RMS Amplitude
The RMS (root-mean-square) amplitude is computed from the square root of
the power spectrum for all spectral components, or equivalently, the amplitude
spectrum divided by the
2
for all ac components. The dc component of
RMS amplitude spectrum is the same as the dc component of the amplitude
spectrum. The FFT calculation produces FFTLen/2 +1 RMS amplitude
components. Spectral binning and ILow and IHigh, described below,