First, we will create a signal to transform. Calculate the Fourier transform with the following steps:
Create a cosine wave with
30
points as follows:x = np.linspace(0, 2 * np.pi, 30) wave = np.cos(x)
Transform the cosine wave with the
fft()
function:transformed = np.fft.fft(wave)
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
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: