import numpy as np
import matplotlib.pyplot as plt

def fourier_transform(data):
    N = len(data)
    n = np.arange(N)
    k = n.reshape((N, 1))
    e = np.exp(-2j * np.pi * k * n / N)
    return np.dot(e, data)

def inverse_fourier_transform(result):
    N = len(result)
    n = np.arange(N)
    k = n.reshape((N, 1))
    e = np.exp(2j * np.pi * k * n / N)
    return np.dot(e, result)

data = np.array([1,1,1,0])

result = fourier_transform(data)

inverse_result = (inverse_fourier_transform(result)) / len(data)
# print(result)

fig, (ax1, ax2) = plt.subplots(1, 2)

ax1.plot(np.abs(result), marker='o', linestyle='', color='b')
print(np.angle(result))
ax1.set_xlabel('Frequency')
ax1.set_ylabel('Magnitude')
ax1.set_title('Discrete Fourier Transform')

ax2.plot(np.abs(inverse_result), marker='o', linestyle='', color='b')
ax2.set_xlabel('Time')
ax2.set_ylabel('Magnitude')
ax2.set_title('Discrete Time Signal')

plt.show()