Campbell Scientific CR5000 Measurement and Control Module - Manual (Page 107)

Section 6. Data Table Declarations and Output Processing Instructions
6-13
Parameter
& Data Type Enter
Units The units for Tau.
Constant Alpha
Code Numeric
Code
Units
USEC 0 microseconds
MSEC 1 milliseconds
SEC 2 seconds
MIN 3 minutes
Options A code to indicate what values to calculate and output.
Constant Code Result
0
1
2
3
4
5
FFT. The output is N/2 complex data points, i.e., the real and
imaginary parts of the FFT. The first pair is the DC component and
the Niquist component. This first pair is an exception because the DC
and niquist components have no imaginary part.
Amplitude spectrum. The output is N/2 magnitudes. With Acos(wt);
A is magnitude.
Amplitude and Phase Spectrum. The output is N/2 pairs of magnitude
and phase; with Acos(wt -
φ
); A is amplitude,
φ
is phase (-
π
,
π
).
Power Spectrum. The output is N/2 values normalized to give a power
spectrum. With Acos(wt -
φ
), the power is A 2 / 2. The summation of
the N/2 values yields the total power in the time series signal.
Power Spectral Density (PSD). The output is N/2 values normalized
to give a power spectral density (power per herz). The Power
Spectrum multiplied by T = N*tau yields the PSD. The integral of the
PSD over a given bandwidth yields the total power in that band. Note
that the bandwidth of each value is 1/T hertz.
Inverse FFT. The input is N/2 complex numbers, organized as in the
output of option 0, which is assumed to be the transform of some real
time series. The output is the time series whose FFT would result in
the input array.
T = N*tau: the length, in seconds, of the time series.
Processing field: “ FFT,N,tau,option” . Tick marks on the x axis are 1/(N*tau)
Hertz. N/2 values, or pairs of values, are output, depending upon the option
code.
Normalization details:
Complex FFT result i, i = 1 .. N/2: ai*cos(wi*t) + bi*sin(wi*t).
wi = 2
π
(i-1)/T.
φ
i = atan2(bi,ai) (4 quadrant arctan)
Power(1) = (a1 2 + b1 2 )/N 2 (DC)
Power(i) = 2*( ai 2 + bi 2 )/N 2 (i = 2..N/2, AC)
PSD(i) = Power(i) * T = Power(i) * N * tau
A1 = sqrt(a1
2 + b1 2 )/N (DC)
Ai = 2*sqrt(ai 2 + bi 2 )/N (AC)