# %%
"""
===================
LTI System Analysis
===================

In this example the state-space, transfer function,
zero-pole-gain, and magnitude response
for an LTI system are derived and visualized.
"""

# %%
# Signal-flow graph
# -----------------
# 6th-order elliptic low-pass filter

from b_asic.sfg_generators.digital_filters import direct_form_2_iir

b = [
    0.00688044, 0.00271194, 0.01334486, 0.00694836,
    0.01334486,0.00271194, 0.00688044
]
a = [
    1, -3.82875342, 7.15331101, -7.94817034,
    5.49500754, -2.23261844,  0.42049185
]

sfg = direct_form_2_iir(b, a)
sfg

# %%
# State-space representation
# --------------------------

ss = sfg.to_ss()
print(ss)

# %%
# Transfer function
# -----------------

tf = sfg.to_tf()
print(tf)

# %%
# Zero-pole-gain
# --------------

zpk = sfg.to_zpk()
zeros, poles, gain = zpk["in0"]
print("Zeros:", zeros)
print("Poles:", poles)
print("Gain:", gain)

# %%
# Pole-zero plot
# --------------

import numpy as np
import matplotlib.pyplot as plt

theta = np.linspace(0, 2 * np.pi, 1024)

fig, ax = plt.subplots()
ax.plot(np.cos(theta), np.sin(theta), "k--")
ax.scatter(zeros.real, zeros.imag, marker="o")
ax.scatter(poles.real, poles.imag, marker="x")
ax.axhline(0, color="black")
ax.axvline(0, color="black")
ax.set_aspect("equal")
ax.set_xlabel("Real")
ax.set_ylabel("Imaginary")
plt.tight_layout()
plt.show()

# %%
# Magnitude response
# ------------------

from b_asic.signal_generator import Impulse
from b_asic.simulation import Simulation

sim = Simulation(sfg, [Impulse()])
sim.run_for(1024)

h = np.array(sim.results["out0"])

H = np.fft.rfft(h)
freqs = np.fft.rfftfreq(len(h))

fig, ax = plt.subplots()
ax.plot(freqs, 20 * np.log10(np.abs(H)))
ax.set_xlabel("Normalized frequency")
ax.set_ylabel("Magnitude, dB")
ax.grid(True)
plt.tight_layout()
plt.show()

# %%