This code represents computing an FFT discrete Fourier in the main part:
np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8)) array([ -3.44505240e-16 +1.14383329e-17j, 8.00000000e+00 -5.71092652e-15j, 2.33482938e-16 +1.22460635e-16j, 1.64863782e-15 +1.77635684e-15j, 9.95839695e-17 +2.33482938e-16j, 0.00000000e+00 +1.66837030e-15j, 1.14383329e-17 +1.22460635e-16j, -1.64863782e-15 +1.77635684e-15j])
In this example, real input has an FFT that is Hermitian, that is, symmetric in the real part and anti-symmetric in the imaginary part, as described in the numpy.fft documentation.
import matplotlib.pyplot as plt t = np.arange(256) sp = np.fft.fft(np.sin(t)) freq = np.fft.fftfreq(t.shape[-1]) plt.plot(freq, sp.real, freq, sp.imag) [<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>] plt.show()
The following screenshot shows how we represent the results:
