import numpy as np
import matplotlib.pyplot as plt
 
def signum(t):
    return np.sign(t)
 
def fourier_transform(t, f):
    dt = t[1] - t[0]
    N = len(t)
    return np.fft.fft(f) * dt, np.fft.fftfreq(N, dt)
 
t = np.linspace(-10, 10, 500, endpoint=False)
f = signum(t)
F, freq = fourier_transform(t, f)
 
plt.figure(figsize=(10, 6))
plt.subplot(2, 1, 1)
plt.plot(t, f)
plt.title('Signum Function')
plt.xlabel('Time')
plt.ylabel('Amplitude')
plt.grid(True)
 
plt.subplot(2, 1, 2)
plt.plot(freq, np.abs(F))
plt.title('Fourier Transform of Signum Function')
plt.xlabel('Frequency')
plt.ylabel('Magnitude')
plt.grid(True)
 
plt.tight_layout()
plt.show()

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