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# %%
import matplotlib.pyplot as plt
import scipy.signal
import numpy as np
import matplotlib
from matplotlib.patches import Rectangle
def ellip_filter(N):
order = N
passband_ripple_db = 3
stopband_attenuation_db = 20
omega_c = 1000
a, b = scipy.signal.ellip(
order,
passband_ripple_db,
stopband_attenuation_db,
omega_c,
btype='low',
analog=True,
output='ba',
fs=None
)
w, mag_db, phase = scipy.signal.bode((a, b), w=np.linspace(0*omega_c,2*omega_c, 4000))
mag = 10**(mag_db/20)
passband_ripple = 10**(-passband_ripple_db/20)
epsilon2 = (1/passband_ripple)**2 - 1
FN2 = ((1/mag**2) - 1)
return w/omega_c, FN2 / epsilon2
plt.figure(figsize=(4,2.5))
for N in [5]:
w, FN2 = ellip_filter(N)
plt.semilogy(w, FN2, label=f"$N={N}$")
plt.gca().add_patch(Rectangle(
(0, 0),
1, 1,
fc ='green',
alpha=0.2,
lw = 10,
))
plt.gca().add_patch(Rectangle(
(1, 1),
0.01, 1e2-1,
fc ='green',
alpha=0.2,
lw = 10,
))
plt.gca().add_patch(Rectangle(
(1.01, 100),
1, 1e6,
fc ='green',
alpha=0.2,
lw = 10,
))
plt.xlim([0,2])
plt.ylim([1e-4,1e6])
plt.grid()
plt.xlabel("$w$")
plt.ylabel("$F^2_N(w)$")
plt.legend()
plt.savefig("F_N_elliptic.pdf")
plt.show()
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