Campbell Scientific CR9000X Measurement and Control System - Manual (Page 304)

Section 8. Processing and Math Instructions
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. The CR9000X computes the psd from:
( )
SR
f N
i r 2 2 2 +
SR
( )
for all components except the dc and Nyquist components. f 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
.
Notes:
• Power is independent of the sampling rate (1/tau) and of the number of
samples (N).
• The PSD is proportional to the length of the sampling period (T=N*tau),
since the “width” of each bin is 1/T.
• The sum of the AC bins (excluding DC) of the Power Spectrum is the
Variance (AC Power) of the time series.
• The factor of 2 in the Power(i) calculation is due to the power series being
mirrored about the Niquist frequency N/(2*T); only half the power is
represented in the FFT bins below N/2, with the exception of DC. Hence,
DC does not have the factor of 2.
• The Inverse FFT option assumes that the data array input is the transform
of a real time series. Filtering is performed by taking an FFT on a data set,
zeroing certain frequency bins, and then taking the Inverse FFT.
Interpolation is performed by taking an FFT, zero padding the result, and
then taking the Inverse FFT of the larger array. The resolution in the time
domain is increased by the ratio of the size of the padded FFT to the size of
the unpadded FFT. This can be used to increase the resolution of a
maximum or minimum, as long as aliasing is avoided.
Floor (Source)
The Floor function rounds a value to a lower number.
Syntax
Variable = Floor( Source )
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