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5b

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 # Q 5B


import numpy as np

from scipy.integrate import quad, simps

from scipy.signal import square, sawtooth

import matplotlib.pyplot as plt


x = np.linspace(-np.pi, np.pi, 1001)

f1 = abs(np.sin(x))

L = 2*np.pi



# Evaluation of Fourier coefficients


a0 = (2.0/L)*simps(f1, x)


an = lambda n: (2.0/L) * simps(f1*np.cos(n*x), x)

bn = lambda n: (2.0/L) * simps(f1*np.sin(n*x), x)



# Summing the serier


R = 10

xn = np.linspace(-R, R, 1001)

s = 0.5*a0 +  sum([an(n)*np.cos(n*xn) + bn(n)*np.sin(n*xn) for n in range(1, 50)])



signal = abs(np.sin(xn))


#Plotting the Functions



plt.plot(xn, signal,'r-' ,label="Original Signal")

plt.plot(xn, s,'ko',ms=2, label = "Fourier Approximation")

plt.legend()

plt.show()

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