Question

Write a computer code using Python, MATLAB∗ or C/C++ to draw the following signals. (a) x(t)=u(2t−1)−u(t+1)

Answer 1

Here's a Python code snippet to plot the signal x(t)=u(2t−1)−u(t+1):

python

import numpy as np

import matplotlib.pyplot as plt

t = np.linspace(-2, 3, 1000)

x = np.heaviside(2*t - 1, 1) - np.heaviside(t + 1, 1)

plt.plot(t, x)

plt.xlabel('t')

plt.ylabel('x(t)')

plt.title('Plot of x(t)=u(2t−1)−u(t+1)')

plt.grid(True)

plt.show()

Step-by-step explanation:

The code utilizes NumPy and Matplotlib libraries in Python. It defines a range of values for 't' using `np.linspace()` from -2 to 3, creating a smooth time axis with 1000 points.

The signal x(t) is calculated using `np.heaviside()` to represent the unit step function. `np.heaviside(2*t - 1, 1)` signifies u(2t−1), and `np.heaviside(t + 1, 1)` represents u(t+1). Subtracting these two step functions gives x(t)=u(2t−1)−u(t+1).

The `plt.plot()` function in Matplotlib generates the plot for x(t) against 't'. Additional commands set labels for the axes, a title for the plot, enable gridlines, and finally display the graph using `plt.show()`.