Time for action – calculating the Fourier transform

First, we will create a signal to transform. Calculate the Fourier transform with the following steps:

1. Create a cosine wave with 30 points as follows:

   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. Apply the inverse transform with the ifft() function. It should approximately return the original signal. Check with the following line:

   print(np.all(np.abs(np.fft.ifft(transformed) - wave) < 10 ** -9))

   The result appears as follows:

   True
   

4. Plot the transformed signal with matplotlib:

   plt.plot(transformed)
   plt.title('Transformed cosine')
   plt.xlabel('Frequency')
   plt.ylabel('Amplitude')
   plt.grid()
   plt.show()

   The following resulting diagram shows the FFT result:

   

What just happened?

We applied the fft() function to a cosine wave. After applying the ifft() function, we got our signal back (see fourier.py):

from __future__ import print_function...