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#!/usr/bin/env python
import numpy as np
import matplotlib.pyplot as plt
import pywt
import pywt.data
ecg = pywt.data.ecg()
# set trim_approx to avoid keeping approximation coefficients for all levels
# set norm=True to rescale the wavelets so that the transform partitions the
# variance of the input signal among the various coefficient arrays.
coeffs = pywt.swt(ecg, wavelet='sym4', trim_approx=True, norm=True)
ca = coeffs[0]
details = coeffs[1:]
print("Variance of the ecg signal = {}".format(np.var(ecg, ddof=1)))
variances = [np.var(c, ddof=1) for c in coeffs]
detail_variances = variances[1:]
print("Sum of variance across all SWT coefficients = {}".format(
np.sum(variances)))
# Create a plot using the same y axis limits for all coefficient arrays to
# illustrate the preservation of amplitude scale across levels when norm=True.
ylim = [ecg.min(), ecg.max()]
fig, axes = plt.subplots(len(coeffs) + 1)
axes[0].set_title("normalized SWT decomposition")
axes[0].plot(ecg)
axes[0].set_ylabel('ECG Signal')
axes[0].set_xlim(0, len(ecg) - 1)
axes[0].set_ylim(ylim[0], ylim[1])
for i, x in enumerate(coeffs):
ax = axes[-i - 1]
ax.plot(coeffs[i], 'g')
if i == 0:
ax.set_ylabel("A%d" % (len(coeffs) - 1))
else:
ax.set_ylabel("D%d" % (len(coeffs) - i))
# Scale axes
ax.set_xlim(0, len(ecg) - 1)
ax.set_ylim(ylim[0], ylim[1])
# reorder from first to last level of coefficients
level = np.arange(1, len(detail_variances) + 1)
# create a plot of the variance as a function of level
plt.figure(figsize=(8, 6))
fontdict = dict(fontsize=16, fontweight='bold')
plt.plot(level, detail_variances[::-1], 'k.')
plt.xlabel("Decomposition level", fontdict=fontdict)
plt.ylabel("Variance", fontdict=fontdict)
plt.title("Variances of detail coefficients", fontdict=fontdict)
plt.show()
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