Specifications

Section 8. Processing and Math Instructions
8-13
Parameter
& Data Type
Enter
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*SampleInterval: the length, in seconds, of the time series.
Processing field: “FFT,N,SampleInterval,option”. Tick marks on the x axis
are 1/(N*SampleInterval) 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 = 2π(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/SampleInterval) and of the
number of samples (N).
• The PSD is proportional to the length of the sampling period
(T=N*SampleInterval), since the “width” of each bin is 1/T.