import numpy as np
import matplotlib.pyplot as plt

# Set scale
# Set sequences
n = np.arange(-1, 6)
x = lambda n: ((1 / 2) ** n) * (n >= 0) * (n <= 3)
y = lambda n: ((1 / 4) ** (n - 1)) * (n >= 0) * (n <= 5)

# Part a
# plt.stem(n, x(n), markerfmt="k.", linefmt="k", basefmt="k")
# plt.title(r"Signal x[n] = $(1/2)^n$, for 0$\leq$n$\leq$3")
# plt.xlabel(r"Index n where 0$\leq$n$\leq$3")
# plt.xticks(n)
# plt.ylabel("Amplitude")

# plt.show()

# plt.stem(n, y(n), markerfmt="k.", linefmt="k", basefmt="k")
# plt.title(r"Signal y[n] = $(1/4)^{n-1}$, for 0$\leq$n$\leq$5")
# plt.xlabel(r"Index n where 0$\leq$n$\leq$5")
# plt.xticks(n)
# plt.ylabel("Amplitude")

# plt.show()

# Part B
plt.stem(n, x(n) * y(n), markerfmt="k.", linefmt="k", basefmt="k")
plt.title(r"Signal x[n]y[n], for 0$\leq$n$\leq$5")
plt.xlabel(r"Index n where 0$\leq$n$\leq$5")
plt.xticks(n)
plt.ylabel("Amplitude")

plt.show()