Time for action – shifting frequencies

We will create a signal, transform it, and then shift the signal. Shift the frequencies with 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. Check with the following code snippet:

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

   The result appears as follows:

   True
   

5. Plot the signal and transform it with matplotlib:

   plt.plot(transformed, lw=2, label="Transformed")
   plt.plot(shifted, '--', lw=3, label="Shifted")
   plt.title('Shifted and transformed cosine wave')
   plt.xlabel('Frequency')
   plt.ylabel('Amplitude')
   plt.grid()
   plt.legend(loc='best')
   plt.show()

   The following diagram...