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I saw a code in Python in the scipy.org (http://docs.scipy.org/doc/scipy-dev/reference/tutorial/fftpack.html) and found this: enter image description here

First question: Is it right that T = 1/800 <==> fs = 800 Hz fulfill the condition fs = 2*fmax, because the maximum frequency of the funtion contains 80 Hz?
Second question is in the row: xf = np.linspace(0.0,1.0/(2.0*T), N/2):
I have often seen that people use the nyquist freqency in the x-axis for the the freqencies spectrum why is that so?
And if I ignore the (1/2 * 1/T) and N/2 and write in my code for xf = np.linspace(0.0, 1.0/T, N) instead of np.linspace(0.0, 1.0/(2.0*T), N/2) so I get a graph like this enter image description here

Why do I get here a mirroring at the 400 Hz? Does it something to do with the symmetries of the fft?
I appreiate it if someone can help me to explain my question, thx alot!

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"Why do I get here a mirroring at the 400 Hz? Does it something to do with the symmetries of the fft?"

yes. the FFT is a "fast" method of computing the DFT. the latter half of the DFT corresponds to what we normally call "negative frequencies" and, for a real signal, the spectrum in the negative frequencies are a complex-conjugate mirror image of the positive frequencies.

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