when I analyse the solution of dynamical system(in time series) by wavelet decomposition, how can I distinguish the differences in figures d1,d2,...,d5?
Wavelet decomposition uses a representation similar to x = sum on i=1...N of (x(i).e(i)), where e(i) would be an orthonormal basis.
So, it's a linear space decomposition, along N (or infinite) dimensions.
That's your starting point.
Look at the e(i), then project on the sub-linear space e(1),...e(n) for n less than N.
With a mathematical eye, it's going to be smoother for you to grasp what you get...
The wavelet decomposition maps a time series into wavelets. Panels d1 to d5 are the results of convolving of the time series with a wavelet which dilates as you go from d1 to d5. As you can see panel d1 shows the higher frequency component and panel d5 shows the lower frequency component.
If you sum the components shown in panels d1 to d5 and add the results with a5, I think you will get the density estimate time series shown in purple.
You can also review the following article which talks about the recent wavelet techniques, dilation, etc.:
Article A Survey on Change Detection and Time Series Analysis with A...
Hope that helps!
Best regards,
Ebrahim
Dear Ebrahim Ghaderpour , Renaud Di Francesco , Aparna Sathya Murthy
thanks for your explanations,
Your descriptions gave me a better understanding of wavelet decomposition.
in wavelet decomposition , when the wavelet level reaches, for example, from 5 to 8(db5 to db8), the accuracy of the answer increases or not, it is not related to the accuracy, it is related to the data.
What will be the effect of raising the wavelet level(db8.png)?
and the other question is that how we analyze the db8 wavelet but with different number of wavelet (not the level of wavelet)in figures db8_1.png and db8_2.png?
(In the graphs, the numbers were marked with a red tick)
what is the differences?
Hi, the following link can be helpful; please see lesson 1:
https://faradars.org/courses/mvrwlt9202-wavelet-transforms-in-matlab
Hi Aparna Sathya Murthy
could you be more specific regarding this phrase about db6 and db10?
the varying number of vanishing moments encodes the coefficients at that corresponding level !!
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