def f(x):
    return np.cos(2*np.pi*x)

#represent noise from a data sample
N = 150
p1 = np.linspace(0.00,0.3,15)
p2 = np.linspace(0.32,0.4,40)
p3 = np.linspace(0.42,1.2,45)
xl = np.concatenate((p1,p2,p3))
np.random.seed(14)
n1 = np.random.normal(0,0.3,15)
n2 = np.random.normal(0,0.1,40)
n3 = np.random.normal(0,0.3,45)
noise = np.concatenate((n1,n2,n3))
y_measured = f(xl) + noise

plt.figure(figsize=(6,3.5))
plt.plot(xl,f(xl),label='source function')
plt.plot(xl,y_measured,'.',label='measured points')
plt.legend()
plt.show()