SciPy Recipes

How it works…

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.