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Q-1B

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 # Q 1B


import numpy as np

import matplotlib.pyplot as plt

from scipy.integrate import simps


a = 1

b = 2


F = lambda t: np.exp(-a*t**2)

F = np.vectorize(F)


G = lambda t: np.exp(-b*t**2)

G = np.vectorize(G)


conv = []


t = np.linspace(-5, 5, 1000)




for i in t:

    t1 = np.linspace(-5.001, i, 1000)

    h = F(t1) * G(i - t1)

    conv.append(simps(h,t1))


plt.plot(t, F(t), label = "F(t)")

plt.plot(t, G(t), label = "G(t)")

plt.plot(t, conv, label = "Convolution")


plt.title("Ques 1B : Verify that convolution of 2 Gaussians is also a Gaussian")

plt.legend()

plt.savefig("1B.png", dpi = 600)

plt.show()


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