# ECG P, T Wave Onset and Peak Detection [ex403.0]#

Example published in [Waldmann2022] as Example 3.

Another common task in cardiology is to accurately measure onsets and peaks of P and T waves in the electrocardiography (ECG) signals. We here demonstrate a Two-Sided Line Model (TSLM) to extract such features.

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import find_peaks

import lmlib as lm

# Constants
K = 2200        # number of samples
sigma = 0.015   # Adding Gaussian Noise
fs = 500        # Sampling Frequency [Hz]
k = range(K)

# load ECG signal as a test signal from library
# y = y1_mc[0:,1] # select single channel

y = y + gen_wgn(K, sigma, seed=233453)*np.concatenate((np.ones(K//2),3*np.ones(K-K//2)))

# cost model to detect events
costs_A = lm.TSLM.create_cost( ab=(-80, 40), gs=(80, 80) )

# Filter
separam_A = lm.RLSAlssm(costs_A)
separam_A.filter(y)

# constraint minimization
x_hat_H1_A = separam_A.minimize_x(lm.TSLM.H_Left_Horizontal)
x_hat_H0_A = separam_A.minimize_x(lm.TSLM.H_Horizontal)

# Square Error and LCR
error_edge_A = separam_A.eval_errors(x_hat_H1_A)
error_line_A = separam_A.eval_errors(x_hat_H0_A)
lcr_A = -1 / 2 * np.log(np.divide(error_edge_A, error_line_A))

# Find LCR peaks with minimal distance and height
# peaks_A, _ = find_peaks(lcr[0:300], height=0.3, distance=50)
peaks_A, _ = find_peaks(lcr_A, height=.25, distance=300)

# Evaluate trajectories (for plotting only)
trajs_edge_A = lm.map_trajectories(costs_A.trajectories(x_hat_H1_A[peaks_A]), peaks_A, K, merge_ks=True)
trajs_line_A = lm.map_trajectories(costs_A.trajectories(x_hat_H0_A[peaks_A]), peaks_A, K, merge_ks=True)

# (B) -- T wave peak Detection -----
costs_B = lm.TSLM.create_cost( ab=(-45, 45), gs=(80, 80) )

# Filter
separam_B = lm.RLSAlssm(costs_B)
separam_B.filter(y)

# constraint minimization
x_hat_H1_B = separam_B.minimize_x(lm.TSLM.H_Peak)
x_hat_H0_B = separam_B.minimize_x(lm.TSLM.H_Horizontal)

# Square Error and LCR
error_edge_B = separam_B.eval_errors(x_hat_H1_B)
error_line_B = separam_B.eval_errors(x_hat_H0_B)
lcr = -1 / 2 * np.log(np.divide(error_edge_B, error_line_B))

# Find LCR peaks with minimal distance and height
peaks_B, _ = find_peaks(lcr, height=.25, distance=150)

# Evaluate trajectories (for plotting only)
trajs_edge = lm.map_trajectories(costs_B.trajectories(x_hat_H1_B[peaks_B]), peaks_B, K, merge_ks=True)
trajs_line = lm.map_trajectories(costs_B.trajectories(x_hat_H0_B[peaks_B]), peaks_B, K, merge_ks=True)

wins = lm.map_windows(costs_B.windows(segment_indices=[1, 1]), peaks_B, K, merge_ks=True)

# -- PLOTTING --
_, axs = plt.subplots(5, 1, figsize=(6, 4), gridspec_kw={'height_ratios': [1.5, 1, 0.1, 1.5, 1]}, sharex='all')
nax = 0

# ----- p onset -----
t = np.array(list(k))/fs

axs[nax].plot(t, y, lw=1.0, c='gray', label='$y$', zorder=0)
if True:
axs[nax].plot(t, trajs_edge_A[0, :], c='k', lw=.75, ls='-', zorder=1, label='$\overrightarrow{s}_{i-k}(\hat x_\ell)$')
axs[nax].plot(t, trajs_edge_A[1, :], c='b', lw=.75, ls='-', zorder=1, label='$\overleftarrow{s}_{i-k}(\hat x_r)$')
axs[nax].scatter(peaks_A[0]/fs, x_hat_H1_A[peaks_A[0], 0], marker='.', c='k', s=20.0)

#axs[nax].axhline(x=peaks_A, ymin=plt.ylim()[0], ymax=plt.ylim()[1])
for xp in peaks_A/fs:
axs[nax].axvline(x=xp, ls='--', c='b', lw=0.5)

#axs[nax].scatter(peaks_A, y[peaks_A], marker=7, c='b')
axs[nax].legend(loc='upper right', labelspacing = -0.0)
axs[nax].set_ylim(bottom=min(y),top=max(y))
nax+=1

axs[nax].plot(t, lcr_A, lw=1.0, c='k', label='LCR')
axs[nax].scatter(peaks_A/fs, lcr_A[peaks_A], marker=7, c='b')
axs[nax].legend(loc=1)
axs[nax].set_ylim(bottom=-0,top=2.2)

# axs[0].set(title='Edge Detection in ECG Signals')

nax+=1
axs[nax].set_visible(False)
nax+=1

t = np.array(list(k))/fs

axs[nax].plot(t, y, lw=1.0, c='gray', label='$y$', zorder=0)
if True:
axs[nax].plot(t, trajs_edge[0, :], c='k', lw=.75, ls='-', zorder=1, label='$\overrightarrow{s}_{i-k}(\hat x_\ell)$')
axs[nax].plot(t, trajs_edge[1, :], c='b', lw=.75, ls='-', zorder=1, label='$\overleftarrow{s}_{i-k}(\hat x_r)$')
axs[nax].scatter(peaks_B[1]/fs, x_hat_H1_B[peaks_B[1], 0], marker='.', c='k', s=20.0)

#axs[nax].axhline(x=peaks_B, ymin=plt.ylim()[0], ymax=plt.ylim()[1])
for xp in peaks_B/fs:
axs[nax].axvline(x=xp, ls='--', c='b', lw=0.5)

#axs[nax].scatter(peaks_B, y[peaks_B], marker=7, c='b')
axs[nax].legend(loc='upper right', labelspacing = -0.0)
axs[nax].set_ylim(bottom=min(y),top=max(y))
nax+=1

axs[nax].plot(t, lcr, lw=1.0, c='k', label='LCR')
axs[nax].scatter(peaks_B/fs, lcr[peaks_B], marker=7, c='b')
axs[nax].legend(loc=1)
axs[nax].set_ylim(bottom=0,top=2.2)

axs[nax].set_xlim(left=.4, right=4.2)

nax+=1
plt.gcf().text(0.883, 0.164, '(s)')