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 # Q 4A

# Fourier Series Sawtooth


import numpy as np

from scipy.signal import sawtooth

from scipy.integrate import simps

import matplotlib.pyplot as plt


t = np.linspace(0,1, 1001)


f1 = sawtooth(2*np.pi*2*t,1)

T = 0.5



#Calculation Of Coefficients


a0 = (2./T) * simps(f1, t)

an = lambda n : (2./T) * simps(f1*np.cos(2*np.pi*2*n*t), t)

bn = lambda n : (2./T) * simps(f1*np.sin(2*np.pi*2*n*t), t)



tn = np.linspace(0, 6, 1001)

s =0.5*a0 + sum([an(n)*np.cos(2*np.pi*2*n*tn) + bn(n)*np.sin(2*np.pi*2*n*tn) for n in range(10)])


plt.plot(tn, s, 'r',label="Fourier approximation")

plt.plot(tn, 2*sawtooth(2*np.pi*2*tn,1) ,label= "Original Signal")

plt.legend()

plt.show()


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