Why are the wavelet coefficients so high at the beginning and at the end of the continuous wavelet analysis in Wavelet Toolbox?

I tried to calculate the CWT with DB3 wavelet using the following commands.

t=0:0.01:100;

y=sin(2*pi*t);

c=cwt(y,1:5,'db3','3Dplot');

Similar wavelets such as symlets and coiflets show the similar results. I would like to know the reason as to why the correlations areso high at these two positions.

Answer 1

[MathWorks Support Team]

This enhancement has been incorporated in Release 2008a (R2008a). For previous product releases, read below for any possible workarounds:

The big coefficients that appear at the beginning and the end of continuous analysis are in fact numerical and theoretical problems:

First, the computations are not continuous but sampled ones, so numerical errors occur.

Second, the signal is finite, and implicitly there is an extension by zeros values. Therefore, there are boundary effects which depend on the wavelet support. For example 'db1' (length of support is 2), the boundary effect appears in scales > 2.

In Chapter 6 of the Wavelet Toolbox documentation it explains that boundary distortions are expected, and this is the reason why there is an opportunity to select the extension modes for a signal before analyzing it. This is explained for the discrete analysis.

The idea is the same for the continuous analysis. If you extend your signal (there are extend functions and GUIs to do that) and then analyze it, you can then recover the central part of the analysis by cutting off the borders and forgetting the edge effects like that.