def problem_3():
f = sy.symbols('f')
psi_hat = wv.battle_lemarie_wavelet_transform()
psi_hat_lambda = sy.lambdify(f, psi_hat, 'numpy')
freq = np.linspace(-2, 2, 100)
freq[0] = np.finfo(float).eps
psi_hat_signal = np.array(np.abs([psi_hat_lambda(v) for v in freq]))
plt.figure()
plt.title('Fourier Transform of Mother Wavelet')
plt.plot(freq, psi_hat_signal)
plt.show()
def problem_4():
# Convert scaling function to time domain
phi_hat = wv.battle_lemarie_scaling_transform()
Xs, ts = f_trans(phi_hat, 8.1, 128, 0)
# Plot scaling function
plt.figure()
plt.subplot(1, 2, 1)
plt.title('Scaling Function')
plt.plot(ts, Xs)
# Convert wavelet to time domain
psi_hat = wv.battle_lemarie_wavelet_transform()
Xs, ts = f_trans(psi_hat, 8.1, 128, 0)
# Plot wavelet
plt.subplot(1, 2, 2)
plt.title('Mother Wavelet')
plt.plot(ts, Xs)
plt.show()