def plot(x, y, db=True):
"""Plot feature and targets"""
from signals.utils import Figure, Subplot
fig = Figure('System Input & Output')
fig.add(Subplot.AmplitudeSpectrum(x, prefix='Input Signal', db=db))
fig.add(Subplot.AmplitudeSpectrum(y, prefix='Output Signal', db=db))
fig.plot()
def define_and_plot(*args, **kwargs):
from signals.generator import multi_tone
from signals.utils import Figure, Subplot
# Initiate model
model = Volterra()
model.set_kernel((0, ), 1.0)
model.set_kernel((2, ), 0.0)
model.set_kernel((0, 0), 0.0)
model.set_kernel((2, 2), 0.0)
model.set_kernel((1, 0, 0), 0.2)
model.set_kernel((2, 2, 2), 0.0)
# Generate multi tone signal
freqs = [160, 220]
signal = multi_tone(freqs, 1000, 2, noise_power=1e-3)
response = model(signal)
# Plot
title = 'Volterra Response, Input freqs = {}'.format(freqs)
fig = Figure(title)
fig.add(Subplot.PowerSpectrum(signal, prefix='Input Signal'))
prefix = 'System Response'
fig.add(Subplot.PowerSpectrum(response, prefix=prefix))
fig.plot()
def plot(self, db=True):
from signals.utils import Figure, Subplot
x = self.signls[0]
y = self.responses[0]
fig = Figure('[{}] System Input & Output'.format(self.name))
fig.add(Subplot.AmplitudeSpectrum(x, prefix='Input Signal', db=db))
fig.add(Subplot.AmplitudeSpectrum(y, prefix='Output Signal', db=db))
fig.plot()
def separate_test(*args, **kwargs):
from signals.generator import multi_tone
from signals.utils import Figure, Subplot
# Initiate model
model = Volterra(degree=3, memory_depth=3)
model.set_kernel((0, ), 1.0)
model.set_kernel((1, ), 0.2)
model.set_kernel((2, ), 0.0)
model.set_kernel((0, 0), 0.0)
model.set_kernel((1, 0), 0.0)
model.set_kernel((1, 1), 0.0)
model.set_kernel((2, 0), 0.1)
model.set_kernel((2, 1), 0.0)
model.set_kernel((2, 2), 0.1)
model.set_kernel((0, 0, 0), 0.0)
model.set_kernel((1, 0, 0), 0.0)
model.set_kernel((1, 1, 0), 0.0)
model.set_kernel((1, 1, 1), 0.001)
model.set_kernel((2, 0, 0), 0.0)
model.set_kernel((2, 1, 0), 0.0)
model.set_kernel((2, 2, 0), 0.002)
model.set_kernel((2, 2, 1), 0.0)
model.set_kernel((2, 2, 2), 0.0)
# Generate multi tone signal
freqs = [160, 220]
signal = multi_tone(freqs, 1000, 2, noise_power=1e-3)
response = model(signal)
max_order = 2
yn = model.separate_interp(signal, max_order=max_order, verbose=True)
truth = model.separate(signal, max_order=max_order)
print('>> rms(response) = {:.4f}'.format(
np.linalg.norm(response) / signal.size))
for n in range(len(yn)):
delta = np.linalg.norm(yn[n] - truth[n]) / signal.size
print(':: Delta_{} = {:.4f}'.format(n + 1, delta))
# Separate Kernel
# Plot
bshow = True
if bshow:
for n in range(len(yn)):
fig = Figure('Volterra Separation order - {}'.format(n + 1))
fig.add(Subplot.PowerSpectrum(response, prefix='response'))
fig.add(
Subplot.PowerSpectrum(truth[n],
prefix='truth order - {}'.format(n + 1)))
fig.add(
Subplot.PowerSpectrum(yn[n],
prefix='pred order - {}'.format(n + 1)))
fig.plot()
def plot(system_output, wiener_output, wiener_delta, vn_output, vn_delta,
homo_str):
form_title = 'Input Frequencies = {}'.format(TEST_FREQS)
fig = Figure(form_title)
# Add ground truth
prefix = 'System Output, $||y|| = {:.4f}$'.format(system_output.norm)
fig.add(Subplot.PowerSpectrum(system_output, prefix=prefix))
# Add
prefix = 'Wiener Output, $||\Delta|| = {:.4f}$'.format(wiener_delta.norm)
fig.add(Subplot.PowerSpectrum(wiener_output, prefix=prefix,
Delta=wiener_delta))
# Add
prefix = 'VN_{:.2f} Output, $||\Delta|| = {:.4f}$'.format(
homo_str, vn_delta.norm)
fig.add(Subplot.PowerSpectrum(vn_output, prefix=prefix, Delta=vn_delta))
fig.plot(ylim=True)
def define_and_plot(*args, **kwargs):
from signals.generator import multi_tone
from signals.utils import Figure, Subplot
# Initiate model
model = Volterra(degree=3, memory_depth=3)
model.set_kernel((0, ), 1.0)
model.set_kernel((1, ), 0.3)
model.set_kernel((2, ), 0.0)
model.set_kernel((0, 0), 0.0)
model.set_kernel((1, 0), 0.0)
model.set_kernel((1, 1), 0.0)
model.set_kernel((2, 0), 0.1)
model.set_kernel((2, 1), 0.0)
model.set_kernel((2, 2), 0.0)
model.set_kernel((0, 0, 0), 0.0)
model.set_kernel((1, 0, 0), 0.0)
model.set_kernel((1, 1, 0), 0.0)
model.set_kernel((1, 1, 1), 0.0)
model.set_kernel((2, 0, 0), 0.0)
model.set_kernel((2, 1, 0), 0.0)
model.set_kernel((2, 2, 0), 0.0)
model.set_kernel((2, 2, 1), 0.0)
model.set_kernel((2, 2, 2), 0.0)
# Generate multi tone signal
freqs = [160, 220]
signal = multi_tone(freqs, 1000, 2, noise_power=1e-3)
order = 2
response = model.inference(signal, order)
delta = np.linalg.norm(signal - response) / signal.size
print('>> Delta = {:.4f}'.format(delta))
# Plot
title = 'Volterra Response, Input freqs = {}'.format(freqs)
fig = Figure(title)
fig.add(Subplot.PowerSpectrum(signal, prefix='Input Signal'))
prefix = 'System Response{}'.format(
' Order-{}'.format(order) if not order is None else '')
response = model(signal) - model.inference(signal, 2)
fig.add(Subplot.PowerSpectrum(response, prefix=prefix))
fig.plot()
def plot_laguerre_3D(alpha=0.2, L=50, contour=True):
from signals.utils import Figure, Subplot
import matplotlib.pyplot as plt
t = np.arange(L + 1)
# x, y = np.meshgrid(t, t)
z = np.zeros(shape=(L + 1, L + 1))
for j in range(L + 1):
z[j] = Laguerre.phi_j(alpha, j, t)
def plot_function(*args):
if contour:
plt.contour(z)
plt.xlabel('Time Units')
plt.ylabel('Order of Laguerre function')
else:
raise NotImplementedError('!! 3D not implemented')
fig = Figure('Discrete Laguerre Functions 3D')
fig.add(Subplot.Custom(plot_function))
fig.plot()
def plot_laguerre(alphas=None, lags=25, js=None):
# Check inputs
if alphas is None: alphas = [0.2, 0.6]
if js is None: js = [0, 1, 2, 3, 4]
t = np.arange(lags + 1)
if not isinstance(alphas, list) and not isinstance(alphas, tuple):
alphas = [alphas]
for alpha in alphas:
if not np.isscalar(alpha) or not 0 < alpha < 1:
raise ValueError(
'!! alpha must be a real number between 0 and 1')
for point in t:
if not point == int(point) >= 0:
raise TypeError(
'!! Each point in t must be a non-negative integer')
# Plot
from signals.utils import Figure, Subplot
fig = Figure('Discrete Orthogonal Laguerre Functions')
title = (r"Laguerre bases $\{\phi_j[n;\alpha]\}$")
for alpha in alphas:
ys = []
legends = []
for j in js:
ys.append(Laguerre.phi_j(alpha, j, t))
legends.append(r'$j = {}$'.format(j))
fig.add(
Subplot.Default(t,
ys,
legends=legends,
xlabel='Time Unit',
title=title +
r', $\alpha = {}$'.format(alpha)))
fig.plot()
wiener_ratio = wiener_delta.norm / system_output.norm * 100
print('>> Wiener err ratio = {:.2f} %'.format(wiener_ratio))
# MLP
mlp_output = mlp(signal)
mlp_delta = system_output - mlp_output
mlp_ratio = mlp_delta.norm / system_output.norm * 100
print('>> MLP err ratio = {:.2f} %'.format(mlp_ratio))
# Plot
if bshow:
form_title = 'Input Frequencies = {}'.format(freqs)
# Input & Output
fig = Figure(form_title)
fig.add(Subplot.PowerSpectrum(signal, prefix='System Input'))
fig.add(Subplot.PowerSpectrum(system_output, prefix='System Output'))
# fig.plot()
# Compare outputs
fig = Figure(form_title)
# fig.add(Subplot.PowerSpectrum(signal, prefix='System Input'))
prefix = 'System Output, $||y|| = {:.4f}$'.format(system_output.norm)
fig.add(Subplot.PowerSpectrum(system_output, prefix=prefix))
prefix = 'Wiener Output, $||\Delta|| = {:.4f}$'.format(wiener_delta.norm)
fig.add(
Subplot.PowerSpectrum(wiener_output, prefix=prefix,
Delta=wiener_delta))
prefix = 'MLP Output, $||\Delta|| = {:.4f}$'.format(mlp_delta.norm)
fig.add(Subplot.PowerSpectrum(mlp_output, prefix=prefix, Delta=mlp_delta))
fig.plot(ylim=(-75, 5))
print(">> Running module system_.py")
fs = 3000
duration = 1
freqs = [500, 800]
vrms = [2, 1]
phases = [0, np.pi]
signal = multi_tone(freqs,
fs,
duration,
vrms=vrms,
phases=phases,
noise_power=1e-3)
def response(input_):
y = np.zeros_like(input_)
for i in range(len(input_)):
x = input_[i]
x_p1 = input_[i - 1] if i != 0 else 0
y[i] = x * x_p1 if x > 0 else 0.4 * x + 0.9 * x_p1
return y
system = System(response)
output = system(signal)
fig = Figure('Input & Output')
db = True
fig.add(Subplot.AmplitudeSpectrum(signal, prefix='Input Signal', db=db))
fig.add(Subplot.AmplitudeSpectrum(output, prefix='Output Signal', db=db))
fig.plot()