Time for action – drawing a square wave

We will initialize t just as in the previous section. We need to sum a number of terms. The higher the number of terms, the more accurate the result; k = 99 should be sufficient. In order to draw a square wave, follow these steps:

  1. We will start by initializing t and k. Set the initial values for the function to 0:
    t = np.linspace(-np.pi, np.pi, 201)
k = np.arange(1, 99)
k = 2 * k - 1
f = np.zeros_like(t)
  2. Compute the function values with the sin() and sum() functions:
    for i, ti in enumerate(t):
   f[i] = np.sum(np.sin(k * ti)/k)

f = (4 / np.pi) * f
  3. The code to plot is almost identical to the one in the previous section:
    plt.plot(t, f)
plt.title('Square wave')
plt.grid()
plt.show()

    The resulting square wave generated with k = 99 is as follows:

    Time for action – drawing a square wave

What just happened?

We generated a square wave or, at least, a fair approximation of it, using the sin() function. The input values were assembled with the linspace() function and the k values with the arange() function (see squarewave.py):

import numpy as np
import matplotlib.pyplot as plt


t = np.linspace(-np.pi, np.pi, 201)
k = np.arange(1, 99)
k = 2 * k - 1
f = np.zeros_like(t)

for i, ti in enumerate(t):
   f[i] = np.sum(np.sin(k * ti)/k)

f = (4 / np.pi) * f

plt.plot(t, f)
plt.title('Square wave')
plt.grid()
plt.show()

Have a go hero – getting rid of the loop

You may have noticed that there is one loop in the code. Get rid of it with NumPy functions and make sure the performance is also improved.

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