Campbell CR9000, Инструкция по эксплуатации

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Section 6. Data Table Declarations and Output Processing Instructions
6-11
Parameter
& Data Type
Enter
FFT Parameters
Source
Variable
The name of the Variable array that contains the input data for the FFT.
DataType
A code to select the data storage format.
Constant Alpha Code Numeric Code Data Format
IEEE4 24 IEEE 4 byte floating point
FP2 7 Campbell Scientific 2 byte floating point
N
Constant
Number of points in the original time series. The number of points must be a power of 2 (i.e., 512, 1024,
2048, etc.).
Tau
Constant
The sampling interval of the time series.
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 herz.
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)
Herz. 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)