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add a demo for of swt variance partitioning when norm=True
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#!/usr/bin/env python | ||
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import numpy as np | ||
import matplotlib.pyplot as plt | ||
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import pywt | ||
import pywt.data | ||
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ecg = pywt.data.ecg() | ||
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# set trim_approx to avoid keeping approximation coefficients for all levels | ||
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# set norm=True to rescale the wavelets so that the transform partitions the | ||
# variance of the input signal among the various coefficient arrays. | ||
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coeffs = pywt.swt(ecg, wavelet='sym4', trim_approx=True, norm=True) | ||
ca = coeffs[0] | ||
details = coeffs[1:] | ||
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print("Variance of the ecg signal = {}".format(np.var(ecg, ddof=1))) | ||
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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))) | ||
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# 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()] | ||
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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]) | ||
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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]) | ||
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# reorder from first to last level of coefficients | ||
level = np.arange(1, len(detail_variances) + 1) | ||
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# 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) |