Does wavelet move a sample point at a time in CWT? This seems to have the best time resolution at all time regardless of what scale is. In the example below, signal length is 2048, for whatever scale value, the calculated coef has a length of 2048.
import pywt
import numpy as np
import matplotlib.pyplot as plt
%matplotlib notebook
# Define signal
fs = 1024.0
dt = 1 / fs
signal_freuqncy = 100
scale = np.arange(2, 256)
wavelet = 'morl'
t = np.linspace(0, 2, int(2 * fs))
y = np.sin(signal_freuqncy*2*np.pi*t)
# Calculate continuous wavelet transform
coef, freqs = pywt.cwt(y, scale, wavelet, dt)
# Show w.r.t. time and frequency
plt.figure(figsize=(6, 4))
plt.pcolor(t, freqs, coef, shading = 'flat', cmap = 'jet')
# Set yscale, ylim and labels
# plt.yscale('log')
# plt.ylim([0, 20])
plt.ylabel('Frequency (Hz)')
plt.xlabel('Time (sec)')
cbar = plt.colorbar()
cbar.set_label('Energy Intensity')
plt.show()
If my guess is right, it is contradictory to my previous understanding that we use expanded wavelet for low freq. component because we want good freq. resolution but poor time resolution at low freq. range. Like shown in the picture.
