import numpy as np
import matplotlib.pyplot as plt

k = 12
h = np.zeros(k)
h[0] = 1
h[1] = -0.5*h[0]
h[2] = -0.5*h[1] + 1

for n in range(3,k-1):
		h[n] = -0.5*h[n-1]

#subplots
plt.stem(range(0,k),h)
plt.title('Impulse Response Definition')
plt.xlabel('$n$')
plt.ylabel('$h(n)$')
plt.grid()# minor

plt.savefig('hndef.png')
