add a demo for of swt variance partitioning when norm=True

Author: grlee77

demo/dwt_swt_show_coeffs.py

@@ -74,7 +74,7 @@ def plot_coeffs(data, w, title, use_dwt=True):
             use_dwt)
 plot_coeffs(ecg, 'sym5', "DWT: Ecg sample - Symmlets5", use_dwt)
 
-# Show DWT coefficients
+# Show SWT coefficients
 use_dwt = False
 plot_coeffs(data1, 'db1', "SWT: Signal irregularity detection - Haar wavelet",
             use_dwt)

demo/swt_variance.py

@@ -0,0 +1,62 @@
+#!/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)