Spectral options, Real and imaginary, Amplitude – Campbell Scientific CR9000X Measurement and Control System User Manual
Page 303: Power
Section 8. Processing and Math Instructions
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)
Spectral Options
The FFTSpa supports the following spectral options.
Real
and
Imaginary
The real and imaginary option returns the raw real (r) and imaginary (i)
components from the FFT. The FFT calculation produces FFTLen/2 +1 pairs of
real and imaginary components.
Amplitude
The amplitude option returns the amplitude of each spectral component. The
FFT calculation produces FFTLen/2 +1 amplitude components. The amplitude
of a sinusoid represented by
( )
t
A
ω
cos
is A. The CR9000X computes the
amplitude from:
N
i
r
2
2
2
+
for all components except the dc and Nyquist components. The dc and Nyquist
components are computed from
N
i
r
2
2
+
N
.
is the Number of points in the original time series. The units of the
amplitude spectrum are mV.
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. 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.
The CR9000X computes the power from:
(
)
2
2
2
2
i
r
+
N
for all spectral components except the dc and Nyquist components. The dc
component is computed from
(
)
2
2
2
i
r
+
N
,
and the Nyquist component is computed from
(
)
2
2
2
2N
i
r
+
.
8-17