Forums

Hilbert-Huang Transformation

Started by waze...@gmail.com April 1, 2009
Anyone heard of it?  Is it the next best thing since sliced bread and
the Fourier Transform?

I just discovered it and it seems to have some interesting
potential...

"The HHT technology is a highly efficient, adaptive, and user-friendly
set of algorithms capable of analyzing time-varying processes.
Designed specifically for nonlinear and nonstationary signals, HHT can
be used to analyze data in a wide variety of applications. The
algorithms also provide increased accuracy when used to analyze linear
and stationary signals.

When linear, stationary datasets are used, HHT provides the same
solution as the Fast Fourier Transform. However, Fourier Transforms
are unsuitable for applications that use nonlinear and/or
nonstationary signals. In addition, other technologies, such as
wavelet transforms, cannot resolve intra-wave frequency modulation,
which occurs in signal systems composed of multiple varying signals.
HHT can be used in these applications to provide an accurate method
for analyzing nonlinear and/or nonstationary signals or data. "

Other info:
http://www.worldscibooks.com/mathematics/etextbook/5862/5862_chap1.pdf
http://en.wikipedia.org/wiki/Hilbert-Huang_Transform
On 1 Apr, 07:44, "wazerf...@gmail.com" <wazerf...@gmail.com> wrote:
> Anyone heard of it? &#2013266080;Is it the next best thing since sliced bread and > the Fourier Transform?
I've heard *of* it, yes. However, I also heard that there are a number of patents involved with the thing, so I never was inclined to find out exactly what this HHT thing is or what it can do. As Donald Knuth once said about patented algorithms: "There are better ways of making a living than preventing other people from benefiting from your discoveries." Or something like that.
> I just discovered it and it seems to have some interesting > potential...
Who wrote the hype? Somebody who has an economical interest in the patents? Rune
Yeah it can be useful.  I used to work at GE and some of our guys were
using it for real actual work.  I don't know if it's the best thing
since sliced bread though.  Here's a paper my former co-worker wrote
that uses it:

Fang, X.; Luo, H. & Tang, J. Investigation of granular damping in
transient vibrations using hilbert transform based technique J.
Vibration and Acoustics, 2008, 130, 31006

wazerface@gmail.com wrote:
> Anyone heard of it? Is it the next best thing since sliced bread and > the Fourier Transform? > > I just discovered it and it seems to have some interesting > potential... > > "The HHT technology is a highly efficient, adaptive, and user-friendly > set of algorithms capable of analyzing time-varying processes. > Designed specifically for nonlinear and nonstationary signals, HHT can > be used to analyze data in a wide variety of applications. The > algorithms also provide increased accuracy when used to analyze linear > and stationary signals. > > When linear, stationary datasets are used, HHT provides the same > solution as the Fast Fourier Transform. However, Fourier Transforms > are unsuitable for applications that use nonlinear and/or > nonstationary signals. In addition, other technologies, such as > wavelet transforms, cannot resolve intra-wave frequency modulation, > which occurs in signal systems composed of multiple varying signals. > HHT can be used in these applications to provide an accurate method > for analyzing nonlinear and/or nonstationary signals or data. " > > Other info: > http://www.worldscibooks.com/mathematics/etextbook/5862/5862_chap1.pdf > http://en.wikipedia.org/wiki/Hilbert-Huang_Transform
On Apr 1, 6:33&#2013266080;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 1 Apr, 07:44, "wazerf...@gmail.com" <wazerf...@gmail.com> wrote: > > > Anyone heard of it? &#2013266080;Is it the next best thing since sliced bread and > > the Fourier Transform? > > I've heard *of* it, yes. However, I also heard that there are a > number > of patents involved with the thing, so I never was inclined to find > out exactly what this HHT thing is or what it can do. > > As Donald Knuth once said about patented algorithms: "There are > better ways of making a living than preventing other people from > benefiting from your discoveries." Or something like that. > > > I just discovered it and it seems to have some interesting > > potential... > > Who wrote the hype? Somebody who has an economical > interest in the patents? > > Rune
:-) Yeah I'm not affiliated with Huang--don't worry! The idea in general seems very interesting though.
On Mar 31, 10:44 pm, "wazerf...@gmail.com" <wazerf...@gmail.com>
wrote:
> Anyone heard of it? Is it the next best thing since sliced bread and > the Fourier Transform?
It depends on whether you are buying it or selling it.
> > I just discovered it and it seems to have some interesting > potential... > > "The HHT technology is a highly efficient, adaptive, and user-friendly > set of algorithms capable of analyzing time-varying processes. > Designed specifically for nonlinear and nonstationary signals, HHT can > be used to analyze data in a wide variety of applications. The > algorithms also provide increased accuracy when used to analyze linear > and stationary signals. > > When linear, stationary datasets are used, HHT provides the same > solution as the Fast Fourier Transform. However, Fourier Transforms > are unsuitable for applications that use nonlinear and/or > nonstationary signals. In addition, other technologies, such as > wavelet transforms, cannot resolve intra-wave frequency modulation, > which occurs in signal systems composed of multiple varying signals. > HHT can be used in these applications to provide an accurate method > for analyzing nonlinear and/or nonstationary signals or data. " > > Other info:http://www.worldscibooks.com/mathematics/etextbook/5862/5862_chap1.pdfhttp://en.wikipedia.org/wiki/Hilbert-Huang_Transform
You sound like you are pitching it, just not very honestly.As a simple rule of thumb, if you want to see iimproper choice of FFT based techniques, see early wavelet papers, If you want to see improper choice of FFT based techniques and improper choice of wavelet based techniques see HHT papers. However, when you see explanations that jump between finite/discrete domains (FFT) and continuous/infinite domains (Fourier Transform) as if the subject hasn't changed, the misrepresentations are often due to ignorance. Dale B. Dalrymple
On 1 Apr., 07:44, "wazerf...@gmail.com" <wazerf...@gmail.com> wrote:
> Anyone heard of it? &#2013266080;Is it the next best thing since sliced bread and > the Fourier Transform? > > I just discovered it and it seems to have some interesting > potential... > > "The HHT technology is a highly efficient, adaptive, and user-friendly > set of algorithms capable of analyzing time-varying processes. > Designed specifically for nonlinear and nonstationary signals, HHT can > be used to analyze data in a wide variety of applications. The > algorithms also provide increased accuracy when used to analyze linear > and stationary signals. > > When linear, stationary datasets are used, HHT provides the same > solution as the Fast Fourier Transform. However, Fourier Transforms > are unsuitable for applications that use nonlinear and/or > nonstationary signals. In addition, other technologies, such as > wavelet transforms, cannot resolve intra-wave frequency modulation, > which occurs in signal systems composed of multiple varying signals. > HHT can be used in these applications to provide an accurate method > for analyzing nonlinear and/or nonstationary signals or data. " >
I wonder what a "nonlinear signal / dataset" is ...
On Apr 1, 3:11&#2013266080;pm, Andor <andor.bari...@gmail.com> wrote:
> On 1 Apr., 07:44, "wazerf...@gmail.com" <wazerf...@gmail.com> wrote: > > > > > > > Anyone heard of it? &#2013266080;Is it the next best thing since sliced bread and > > the Fourier Transform? > > > I just discovered it and it seems to have some interesting > > potential... > > > "The HHT technology is a highly efficient, adaptive, and user-friendly > > set of algorithms capable of analyzing time-varying processes. > > Designed specifically for nonlinear and nonstationary signals, HHT can > > be used to analyze data in a wide variety of applications. The > > algorithms also provide increased accuracy when used to analyze linear > > and stationary signals. > > > When linear, stationary datasets are used, HHT provides the same > > solution as the Fast Fourier Transform. However, Fourier Transforms > > are unsuitable for applications that use nonlinear and/or > > nonstationary signals. In addition, other technologies, such as > > wavelet transforms, cannot resolve intra-wave frequency modulation, > > which occurs in signal systems composed of multiple varying signals. > > HHT can be used in these applications to provide an accurate method > > for analyzing nonlinear and/or nonstationary signals or data. " > > I wonder what a "nonlinear signal / dataset" is ...- Hide quoted text - > > - Show quoted text -
Nonlinear, I believe, refers to general signals that start and stop (short duration). In the 1980's the Wigner Transform was going to solve all problems of detecting short-term waveforms and their location in time with precision. Anyone here actually apply it? It didn't catch on. IIRC, one problem was you had to analyze the data until after the event to be sure the changes observed were part of the kind of event you were looking for. So there was a potentialy significant delay in the detection, and a lot of calculation. Oh well, everything was going to solved back then with AI anyway (implemented as shitloads of if statements).
On 1 Apr, 22:51, spamfreecomp...@gmail.com wrote:
> &#2013266080;In the 1980's the Wigner Transform was going to > solve all problems of detecting short-term waveforms and their > location in time with precision. &#2013266080;Anyone here actually apply it?
Sort of; a fellow student of mine used the Wigner-Ville Transform to estimate dispersive properties of seismic waves. I tried to solve the same task by (f,k) decompositions of the data. The baseline was a regular filter bank analysis of the same data. The WVT actually performed worse than the baseline, in that it showed all the weaknesses of the filterbanks (weak signals hidden in noise or masked by strong signals, resolution issues in both time and frequency) in addition to some of its own. One main drawback was that if you had sequences of wavelets, as we did, you also got cross terms in the WVT data. So you had the added problem of figuring out what was useful data, and what was cross terms. Very educational, but hardly useful.
>&#2013266080;It > didn't catch on.
Go figure... Rune
On Apr 1, 4:43&#2013266080;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 1 Apr, 22:51, spamfreecomp...@gmail.com wrote: > > > &#2013266080;&#2013266080;In the 1980's the Wigner Transform was going to > > solve all problems of detecting short-term waveforms and their > > location in time with precision. &#2013266080;Anyone here actually apply it? > > Sort of; a fellow student of mine used the Wigner-Ville Transform > to estimate dispersive properties of seismic waves. I tried to solve > the same task by (f,k) decompositions of the data. The baseline > was a regular filter bank analysis of the same data. > > The WVT actually performed worse than the baseline, in that it > showed all the weaknesses of the filterbanks (weak signals > hidden in noise or masked by strong signals, resolution issues > in both time and frequency) in addition to some of its own. > One main drawback was that if you had sequences of wavelets, > as we did, you also got cross terms in the WVT data. > So you had the added problem of figuring out what was > useful data, and what was cross terms. Very educational, > but hardly useful. > > >&#2013266080;It > > didn't catch on. > > Go figure... > > Rune
Yes for WV you must apply some kernel function to eliminate the cross- terms if you don't want interference. This of course lowers your resolution.
On Apr 1, 1:44&#2013266080;pm, dbd <d...@ieee.org> wrote:
> On Mar 31, 10:44 pm, "wazerf...@gmail.com" <wazerf...@gmail.com> > wrote: > > > Anyone heard of it? &#2013266080;Is it the next best thing since sliced bread and > > the Fourier Transform? > > It depends on whether you are buying it or selling it. > > > > > > > I just discovered it and it seems to have some interesting > > potential... > > > "The HHT technology is a highly efficient, adaptive, and user-friendly > > set of algorithms capable of analyzing time-varying processes. > > Designed specifically for nonlinear and nonstationary signals, HHT can > > be used to analyze data in a wide variety of applications. The > > algorithms also provide increased accuracy when used to analyze linear > > and stationary signals. > > > When linear, stationary datasets are used, HHT provides the same > > solution as the Fast Fourier Transform. However, Fourier Transforms > > are unsuitable for applications that use nonlinear and/or > > nonstationary signals. In addition, other technologies, such as > > wavelet transforms, cannot resolve intra-wave frequency modulation, > > which occurs in signal systems composed of multiple varying signals. > > HHT can be used in these applications to provide an accurate method > > for analyzing nonlinear and/or nonstationary signals or data. " > > > Other info:http://www.worldscibooks.com/mathematics/etextbook/5862/5862_chap1.pd... > > You sound like you are pitching it, just not very honestly.As a simple > rule of thumb, if you want to see iimproper choice of FFT based > techniques, see early wavelet papers, If you want to see improper > choice of FFT based techniques and improper choice of wavelet based > techniques see HHT papers. However, when you see explanations that > jump between finite/discrete domains (FFT) and continuous/infinite > domains (Fourier Transform) as if the subject hasn't changed, the > misrepresentations are often due to ignorance. > > Dale B. Dalrymple
Yes my quote came from the NASA website: http://techtransfer.gsfc.nasa.gov/HHT/ and they _are_ pitching it!