from scipy.fftpack import dct, idct
import matplotlib.pyplot as plt
N = 100
t = np.linspace(0,20,N)
x = np.exp(-t/3)*np.cos(2*t)
y = dct(x, norm='ortho')
window = np.zeros(N)
window[:20] = 1
yr = idct(y*window, norm='ortho')
sum(abs(x-yr)**2) / sum(abs(x)**2)
# 0.0010901402257
plt.plot(t, x, '-bx')
plt.plot(t, yr, 'ro')
window = np.zeros(N)
window[:15] = 1
yr = idct(y*window, norm='ortho')
sum(abs(x-yr)**2) / sum(abs(x)**2)
# 0.0718818065008
plt.plot(t, yr, 'g+')
plt.legend(['x', '$x_{20}$', '$x_{15}$'])
plt.grid()
plt.show()