For the graph shown in Figure 11.1, compute the wavelets centered at node 1 and at scales t = 2, 10, and 40. Use the same kernel given by Equation (11.7.7). Comment on the wavelets at different scales.
What will be an ideal response?
The wavelets at scales 2, 10, and 40 are shown in Figure 11.8. We can see that all the three
kernels at these scales are concentrated at low frequencies. Therefore, the wavelets at these
scales does not differentiate in terms of the spread. However, if we compute the wavelets
at scales 0.1146, 0.5126, and 2.2922, we get wavelets with different spreads. These wavelets
are shown in Figure 11.9. Therefore, we should carefully choose the scales. These scales are
chosen as described in Section 11.7.2 of the book.
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