Campbell Scientific CR9000X Measurement and Control System User Manual
Page 199
Section 6. Data Table Declarations and Output Processing Instructions
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.
φi = 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)
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 Nyquist frequency N/(2*T); only half the power is
represented in the FFT bins below N/2, with the exception of DC
component. 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 can be performed by performing 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.
6-15