fourier series coefficients in python

main.py
import numpy as np
import math
import matplotlib.pyplot as plt

# Define the function to be analyzed (a square wave)
def square_wave(x):
    y = np.zeros(len(x))
    for i in range(len(x)):
        if np.sin(x[i]) >= 0:
            y[i] = 1
        else:
            y[i] = -1
    return y

# Create time and frequency arrays
t = np.linspace(0, 2*np.pi, 1000)
dt = t[1] - t[0]
f = np.linspace(-1/(2*dt), 1/(2*dt), len(t))

# Compute the Fourier coefficients
y = square_wave(t)
Y = np.fft.fftshift(np.fft.fft(y))/len(y)

# Generate the Fourier series
n = len(y)
y_ift = np.zeros_like(y)
for i in range(n):
    y_ift += Y[i]*np.exp(2*math.pi*1j*i*np.arange(n)/n)

# Plot the original function and the Fourier series approximation
plt.plot(t, y, label='original function')
plt.plot(t, y_ift.real, label='Fourier series')
plt.legend()
plt.show()
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