Square signal without for loops

ditch-for-loops.py

import numpy as np

# first define our input values and all values for k
t = np.linspace(0, 1, 200) 
k = np.arange(0, 1000)
f = 10 # frequency in Hertz

# from the formula, isolate all factors in the sinus term which include k
k = 2 * np.pi * (2 * k - 1) * f

# then construct a helper matrix in shape (200, 1000)
tk = np.outer(t, k)

# apply the rest of the multiplicative terms in the sum
F = np.sin(tk) / (2 * k - 1)

# then sum along the k axis, resulting in an array (200,)
res = np.sum(F, axis=1) 
res *= (4 / np.pi)