Why does fftfreq produce negative values?

From the documentation for fftfreq:

>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
>>> fourier = np.fft.fft(signal)
>>> n = signal.size
>>> timestep = 0.1
>>> freq = np.fft.fftfreq(n, d=timestep)
>>> freq
array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])

Why are there negative values in the output array?

I am trying to produce a plot of amplitude vs frequency. I can get the amplitude by running the abs() function over the elements of fourier, but how do I convert freq into a series of frequencies that I can use as an x-axis when plotting fourier?

Answer

It’s inherent to FFT algorithm. The second half of FFT array is the conjugate of the first half, so don’t contain any new information.

To visualize the spectrum, just use the first half.

f=freq[:n/2]
s=abs(fourier[:n/2])
plot(f,s)