Time for action – shifting frequencies

We will create a signal, transform it, and then shift the signal. In order to shift the frequencies, perform the following steps:

1. Create a cosine wave with 30 points.

   x =  np.linspace(0, 2 * np.pi, 30)
   wave = np.cos(x)

2. Transform the cosine wave with the fft function.

   transformed = np.fft.fft(wave)

3. Shift the signal with the fftshift function.

   shifted = np.fft.fftshift(transformed)

4. Reverse the shift with the ifftshift function. This should undo the shift.

   print np.all((np.fft.ifftshift(shifted) - transformed) < 10 ** -9)

   The result is shown as follows:

   True
   

5. Plot the signal and transform it with Matplotlib.

   plot(transformed, lw=2)
   plot(shifted, lw=3)
   show()

   The following screenshot shows the shift in the fast Fourier transform:

   

What just happened?

We applied the fftshift function to a cosine wave. After applying the ifftshift function, we got our signal back (see fouriershift.py).

import numpy as np
from matplotlib.pyplot import plot, show

x =  np.linspace(0...