Constrained fit of sinusoidal models to ECG signal [ex901.0]

Out:

(4, 550)

import matplotlib.pyplot as plt
import numpy as np
import lmlib as lm
from lmlib.utils.generator import gen_sine, gen_wgn, load_multi_channel

# --- Generating Test signal ---
K = 550
NOISE = .05

OMEGA = 0.07 # frequency
k = np.arange(K)


if True: # ecg test signal
    k_start = 180
    y1_mc = load_multi_channel('EECG_FILT_9CH_10S_FS600HZ.csv', K=K+k_start)
    y1 = y1_mc[k_start:,1] # select single channel
    yn = gen_wgn(K, .01, seed=1234)






# ----- Models and Parameter Estimation  --------------

# Sinusoidal ALSSM
alssm_poly = lm.AlssmSin(omega=OMEGA)
# Segment
segment = lm.Segment(a=0, b=int(np.floor(np.pi/OMEGA)), direction=lm.BACKWARD, g=5000)

# CostSeg
costs = lm.CostSegment(alssm_poly, segment)


# filter signal and take the approximation
y = y1 + yn*NOISE
se_param = lm.SEParam(costs)
se_param.filter(y)

xs = se_param.minimize_x() # unconstrained minimization

H = [[0],
     [1]]
xs0 = se_param.minimize_x(H) # constrained minimization

H = [[1],
     [0]]
xs1 = se_param.minimize_x(H) # constrained minimization


# ----------------  Plot  -----------------
ks = [25,  140, 300, 500] # indeces to display fit

trajs = lm.map_trajectories(costs.trajectories(xs[ks], thd=0.1), ks, K)
trajs0 = lm.map_trajectories(costs.trajectories(xs0[ks], thd=0.1), ks, K)
trajs1 = lm.map_trajectories(costs.trajectories(xs1[ks], thd=0.1), ks, K)

wins = lm.map_window(costs.window(), ks, K)



# axs[0].set( title='noise: $\sigma ='+str(NOISE)+'$')


fig = plt.figure(figsize=(8,3))

axs = fig.add_subplot(3, 1, 1)
print(wins.shape)
lss = ['--', '-', ':','-.','--']
for (n, _) in enumerate(ks):
    axs.plot(k, wins[n,:], lw=1, c='k', ls=lss[n])

axs.set( ylabel='window(s)')


axs = fig.add_subplot(3, 1, (2,3))
axs.plot(k, y, lw=1.0, c='tab:gray')

# for n in range(0,np.shape(trajs)[1]):
for (n, traj) in enumerate(trajs[:,:,0]):
    axs.plot(k, traj, lw=1.5, c='k', ls='-', label='$a_0 cos(i \Omega) - a_1 sin(i \Omega)$' if n==0 else '')
    axs.scatter(ks[n], traj[ks[n]], marker='x', c='k')
    axs.plot(k, trajs0[n, :, 0], lw=1.5, c='k', ls='--', label='$a_0 cos(i \Omega)$' if n == 0 else '')
    axs.scatter(ks[n], trajs0[n, ks[n], 0], marker='x', c='k')
    axs.plot(k, trajs1[n, :, 0], lw=1.5, c='k', ls='-.', label='$-a_1 sin(i \Omega)$' if n == 0 else '')
    axs.scatter(ks[n], trajs1[n, ks[n], 0], marker='x', c='k')
axs.grid(True)
# axs[1].set_ylim([-3, 3])
axs.legend(loc='upper right')

plt.subplots_adjust(hspace=0.4)

plt.show()

Constrained fit of sinusoidal models to ECG signal [ex901.0] Detecting of binary signal, LCR (Skeleton) [ex910.0]