skeleton Hilbert transform (emd, hht)

I am interested in applying the EMD (empirical mode decomposition)
algorithm to some speech signals.  I note in some of the papers, e.g.,
"The empirical mode decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series," that authors display the
skeleton Hilbert transform of the IMFs (intrinsic mode functions).  Can
someone explain how I can obtain the skeleton Hilbert transform, esp.
in terms of Matlab functions?

Thanks!
Marcus

magoldfish@gmail.com wrote:
> I am interested in applying the EMD (empirical mode decomposition)
> algorithm to some speech signals.  I note in some of the papers, e.g.,
> "The empirical mode decomposition and the Hilbert spectrum for
> nonlinear and non-stationary time series," that authors display the
> skeleton Hilbert transform of the IMFs (intrinsic mode functions).  Can
> someone explain how I can obtain the skeleton Hilbert transform, esp.
> in terms of Matlab functions?

Calculate IA and IF for each IMF and plot IA(IF,t)^2 (energy)

On 9 Feb 2006 16:05:42 -0800, magoldfish@gmail.com wrote:

>I am interested in applying the EMD (empirical mode decomposition)
>algorithm to some speech signals.  

(snipped)
>
>Marcus
>

Hi Marcus,

  I've read a tiny bit about EMD, but not nearly 
enough to understand it subtleties.

Marcus, do you think, based on your experience, 
that EMD is something that the "average" DSP 
engineer should study?  In different words, do 
you think the benefits from learning EMD outweigh 
the trouble it takes to learn about this 
process?

Thanks,
[-Rick-]

  

Rick Lyons <R.Lyons@_bogus_ieee.org> wrote:
> On 9 Feb 2006 16:05:42 -0800, magoldfish@gmail.com wrote:
> 
>>I am interested in applying the EMD (empirical mode decomposition)
>>algorithm to some speech signals.  
> 
> (snipped)
>>
>>Marcus
>>
> 
> Hi Marcus,
> 
>  I've read a tiny bit about EMD, but not nearly 
> enough to understand it subtleties.
> 
> Marcus, do you think, based on your experience, 
> that EMD is something that the "average" DSP 
> engineer should study?  In different words, do 
> you think the benefits from learning EMD outweigh 
> the trouble it takes to learn about this 
> process?

Hmm, I found very long thread about EMD on Chinese www-board. I can't read
it ;) but starting from page:

  http://www.lasg.ac.cn/cgi-bin/forum/topic.cgi?forum=2&topic=2269&start=210

there are some fragments in english. 

It can be summarized:
a) EMD lacks theoretical foundations
b) non-orthogonality gives many troubles
c) a free stopping parameter gives unpredictable results
d) kidding research about statistical properties of EMD
d) they suppose that papers about EMD-HHT results (even orignal Huang's from
   1998) are done with some unethical manipulations.

Even if EMD (the sifting process) can be done in a robust manner - Huang
stated somewhere that only the NASA implementation gives proper results -
there are other theoretical problems with IMF's. You can read Vesselin's
papers:
  http://www.waveletidr.org/workshop6/talks/vatchev.pdf
  http://www.math.sc.edu/~IMI/technical/04papers/0412.pdf

> Hi Marcus,
>
>   I've read a tiny bit about EMD, but not nearly
> enough to understand it subtleties.
>
> Marcus, do you think, based on your experience,
> that EMD is something that the "average" DSP
> engineer should study?  In different words, do
> you think the benefits from learning EMD outweigh
> the trouble it takes to learn about this
> process?
I think it depends on the types of signals you are interested in
studying, and whether the applications are commercial.

The intuition behind the EMD is pretty cool-- decompose a signal into a
sum of zero-mean AM-FM components-- and the algorithm is incredibly
easy to understand.  Unlike Fourier or wavelet analysis, the bases
functions (imfs) are adaptive, and data-dependent.  Huang and others
argue that this gives emd an advantage for non-stationary, nonlinear
signal analysis.  They report some amazing results in their papers.
And you can always try it out with the free matlab toolbox from:

http://perso.ens-lyon.fr/patrick.flandrin/emd.html

However, as another poster points out, perhaps somewhat too negatively,
the theory greatly lags the success of applications.  Also, the
algorithm is very slow compared to FFTs.  Finally, Huang (NASA) have at
least one patent on it, so it may not be suitable for commercial
applications.

Marcus

On 16 Feb 2006 17:19:46 -0800, magoldfish@gmail.com wrote:

>> Hi Marcus,
>>
>>   I've read a tiny bit about EMD, but not nearly
>> enough to understand it subtleties.
>>
>> Marcus, do you think, based on your experience,
>> that EMD is something that the "average" DSP
>> engineer should study?  In different words, do
>> you think the benefits from learning EMD outweigh
>> the trouble it takes to learn about this
>> process?
>I think it depends on the types of signals you are interested in
>studying, and whether the applications are commercial.
>
>The intuition behind the EMD is pretty cool-- decompose a signal into a
>sum of zero-mean AM-FM components-- and the algorithm is incredibly
>easy to understand.  Unlike Fourier or wavelet analysis, the bases
>functions (imfs) are adaptive, and data-dependent.  Huang and others
>argue that this gives emd an advantage for non-stationary, nonlinear
>signal analysis.  They report some amazing results in their papers.
>And you can always try it out with the free matlab toolbox from:
>
>http://perso.ens-lyon.fr/patrick.flandrin/emd.html
>
>However, as another poster points out, perhaps somewhat too negatively,
>the theory greatly lags the success of applications.  Also, the
>algorithm is very slow compared to FFTs.  Finally, Huang (NASA) have at
>least one patent on it, so it may not be suitable for commercial
>applications.
>
>Marcus

  Hi Marcus,

  Thanks to you 
(and the mysterious pisz_na.mirek@dionizos.zind.ikem.pwr.wroc.pl) 
for your thoughts and opinions regarding the EMD algorithm.

I know that NASA touted the EMD algorithm as 
an important breakthrough in signal analysis,
but it's nice to receive the real-world, practical, 
opinions from you guys.

Thanks again & Regards,
[-Rick-]