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> Volume 7, Issue 11
Answer: Decomposition Tree for Wavelet Packets (WD 7.8 #26)

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Dennis Lee (dennis.lee@eng.monash.edu.au) Guest

Posted: Sun Oct 18, 1998 12:44 am Subject: Answer: Decomposition Tree for Wavelet Packets (WD 7.8 #26)




#15 Answer: Decomposition Tree for Wavelet Packets (WD 7.8 #26)
Question: How to the decomposition tree level for wavelet packets
> Application of wavelet packets to fault diagnosis for feature extraction
> Many examples using wavelet packets are chosen of decompostion tree
> level 3 or 4 for signal analysis. Is there any mathematcal theory or
> other references to explain the proper procedure to correctly select
> decomposition tree level of wavelet packets ?
Thank you for many experts to give valuable answers that are unlikely to
display all. A short summary of the two is listed below. I apology for
any missing answers sincerely.
Dennis Lee
Electrical and Computer Systems Dept.
Monash University
email: dennis.lee@eng.monash.edu.au
**** Answer no.1 from Andy
I found that by reconstructing the original signal with only the level
in question (all other wavelet levels equivalent to zero) and then
performing standard Fourier analysis on the reconstructed signal, it
could be seen that the wavelet analysis was in fact acting like a
filter on the signal, with each wavelet level corresponding to a
different frequency band in the original signal. Therefore, if you
have any knowledge of the particular frequencies you should be looking
at, you can use this as a guideline for the correct wavelet level.
Alternatively, this type of analysis can point you in the direction of
the most important frequencies in your signal.
This should explain why level 3 works but not level 4 (for example) 
since each wavelet level is in fact filtering out different frequency
bands.
Andy Starkey
Dept of Engineering
Fraser Noble Building
University of Aberdeen
**** Answer no. 2 from Sherman
I think the rule of choosing proper decomposition level is depends on
the characteristic of your signal. If the signal was generated from
lots of excitation components, you will like to have higher level of
decomposition. Each level corresponding to its frequency range. So,
if you knows about your signal a lot, you will know which level will
be more sensitive to its change of amplitude.
Sherman ChaoShih Liu
Mechanical Engineering, U. of Washington 





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