Fourier Square Wave.py

import numpy as np

import matplotlib.pyplot as plt

from scipy.signal import square

from scipy.integrate import quad

from math import* #import all function from math

x=np.arange(-np.pi,np.pi,0.001) # x axis has been chosen from –π to +π, value of 1 smallest square along x axis is 0.001 

y=square(x) #defining square wave function 𝑦 =−1, 𝑓𝑜𝑟 − 𝜋 ≤ 𝑥 ≤ 0
#y= +1, 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 𝜋

#define fuction

fc=lambda x:square(x)*cos(i*x)  #i :dummy index

fs=lambda x:square(x)*sin(i*x)

n=50 #max value of I, not taken infinity, better result with high value

An=[] # defining array

Bn=[]

sum=0

for i in range(n):

 an=quad(fc,-np.pi,np.pi)[0]*(1.0/np.pi)

 An.append(an)

for i in range(n):

 bn=quad(fs,-np.pi,np.pi)[0]*(1.0/np.pi)

 Bn.append(bn) #putting value in array Bn

for i in range(n):

 if i==0.0:
     sum=sum+An[i]/2

 else:
     sum=sum+(An[i]*np.cos(i*x)+Bn[i]*np.sin(i*x))

plt.plot(x,sum,'g')

plt.plot(x,y,'r--')

plt.title("fourier series for square wave")

plt.show()