I’ve got a question concerning the definition of the frequency array and the FFT usage. For simplicity, let’s assume that:
Nx = 4096;
T = 600 [s];
This means that the Nyquist frequency (or cut-off frequency) is
fn = Nx/T = 4096/600 [Hz] = 6.82667 [Hz];
while the minimum frequency value will be
fmin = 1/600 [Hz] = 0.00167 [Hz]
Generally, for FFT application’s purposes, I would define a frequency vector which spans between -fn/2 and b/2[/b].
In the end, by using a frequency vector such as the one mentioned above, for each simulation I would get two time series: one due to the real components and one due to the imaginary component.
But, generally and especially in our case, we can take advantage of this FFT feature, defining only half of the frequency vector: in the end, imaginary and real part of the FFT will be merged and retrieve our desired 4096 sample time series (for each of the grid point of course).
It seems to me that TurbSim makes use of such a procedure; my question concerns therefore the definition of the frequency range: how shall I define it properly? At the moment I would do this:
f = (0:2048)*0.00167;
But this vector contains 2049 elements and when merging real and imaginary part, the zero order is counted twice.
Would you mind to give me a hunch?
I warmly thank you in advance and look forward to hearing from you.