import numpy as np
import matplotlib.pyplot as plt
import scipy as sp

f_s = 8E3

T_s = 1/f_s
t = np.arange(-5,5,T_s)

f = np.linspace(0,f_s,len(t))
omega = 2*np.pi*f

def u(t):
    return np.heaviside(t, 1)

w = u(t) - u(t-0.6) + u(t-0.7) - u(t-1)

W_c = 1j*(np.exp(-1j*omega*0.6) + np.exp(-1j*omega) - np.exp(-1j*omega*0.7) - 1)/omega
W_d = sp.fft.fft(w)

print(W_c[:10])
print(W_d[:10])


plt.plot(t,w)
plt.show()


plt.subplot(211)
plt.plot(W_c)
plt.subplot(212)
plt.plot(W_d)
plt.show()