EMD-Empirical Mode Decomposition

Hello.

I have a question and hope someone can help me. I'm dealing with the EMD
since a few weeks and have a problem with one aspect.

The first step is to identify all the local extrema in the test data x. My
question is the following:

Is every extreme I find, a real extreme? I have for example sinus signal
that is superimposed by noise. So it might be, that I found a lot of
extreme values sequently. I have for example a maximum on the position x(5)
and a minimum on x(6) and on x(7) again a maximum. Is that right, or shall
I eliminate the extreme on x(6)? And must all Maxima be positiv and all
Minima be negativ?

I hope someone can help me. Sorry for my english. English isn't my mother
tongue. I hope you still understand me.

Best regards
Joanna

On 10/24/2011 11:49 AM, joanna wrote:
> Hello.
>
> I have a question and hope someone can help me. I'm dealing with the EMD
> since a few weeks and have a problem with one aspect.
>
> The first step is to identify all the local extrema in the test data x. My
> question is the following:
>
> Is every extreme I find, a real extreme? I have for example sinus signal
> that is superimposed by noise. So it might be, that I found a lot of
> extreme values sequently. I have for example a maximum on the position x(5)
> and a minimum on x(6) and on x(7) again a maximum. Is that right, or shall
> I eliminate the extreme on x(6)? And must all Maxima be positiv and all
> Minima be negativ?
>
> I hope someone can help me. Sorry for my english. English isn't my mother
> tongue. I hope you still understand me.

Joanna,

Your question is perfectly clear. Your use of English is in fact quite 
good. I wish most Americans spoke a foreign language as well as you 
write English.

You ask for a definition of extremum that must depend on your 
application. With noisy data, the rule "A point both of whose neighbors 
are larger is a minimum, and both of whose neighbors are smaller is a 
maximum" clearly needs to be modified. You ask what modification is 
correct. There is probably no correct way, only a best compromise that 
depends on what the results are used for.

Do you need results as the data are being collected, or can you wait?

Local minima can be positive and local maxima can be negative by the 
most general definition. You may have other constraints.

One way I dealt with your problem -- I had the luxury of analyzing data 
already collected and stored -- was by smoothing the data with a 
low-pass filter, finding extrema in the usual way, then referring the 
corrected* time of of the extremum back to the original data.
_____________________
* Filtering delays the data. It also corrupts the beginning and end for 
a time equal to about double the delay.)

Jerry
-- 
Engineering is the art of making what you want from things you can get.

Hi ,

>One way I dealt with your problem -- I had the luxury of analyzing data 
>already collected and stored -- was by smoothing the data with a 
>low-pass filter, finding extrema in the usual way, then referring the 
>corrected* time of of the extremum back to the original data.
>_____________________

exactly the same way I done it. I'm relieved that my idea wasn't so bad.

But I have another question. When I compute the instanteanous frequency I
receive also negative frequencies.

What shall I do with them?

Best regards
Joanna

On 10/25/2011 10:14 AM, joanna wrote:
> Hi ,
>
>> One way I dealt with your problem -- I had the luxury of analyzing data
>> already collected and stored -- was by smoothing the data with a
>> low-pass filter, finding extrema in the usual way, then referring the
>> corrected* time of of the extremum back to the original data.
>> _____________________
>
> exactly the same way I done it. I'm relieved that my idea wasn't so bad.
>
> But I have another question. When I compute the instanteanous frequency I
> receive also negative frequencies.
>
> What shall I do with them?

Whatever one might believe about the actual existence of negative 
frequencies, they are part of the simplified mathematics that we use in 
our calculations. That is, replacing trigonometry with complex 
arithmetic by replacing cos(x) with ((exp(ix) + exp(-ix))/2 introduces 
negative frequencies into our work. (Note the exp(-ix).)

Nevertheless, I remain puzzled. You have a series in the time domain. 
You want extrema, which are time-domain phenomena. Why involve frequency?

Frequency is the rate at which phase changes. The nature of inverse trig 
functions can make a plot of phase vs. time appear to be discontinuous. 
For accurate calculations "everywhere", the phase needs to be 
"unrolled". Are there phase discontinuities in the interval you use for 
differentiating?

Jerry
-- 
Engineering is the art of making what you want from things you can get.

I think there are no phase discontinuities. I compute the phase in matlab
with this:

phase = unwrap(angle(z));

z is the analytic signal. unwrap corrects phase angles to produce smoother
phase plots. I dont't know if that means that i dont't have phase
discontinuities. My know-how in signal prosessing isn't so big :-)

I hope this answear helps ?!?

On 10/25/2011 11:02 AM, joanna wrote:
> I think there are no phase discontinuities. I compute the phase in matlab
> with this:
>
> phase = unwrap(angle(z));
>
> z is the analytic signal. unwrap corrects phase angles to produce smoother
> phase plots. I dont't know if that means that i dont't have phase
> discontinuities. My know-how in signal prosessing isn't so big :-)
>
> I hope this answear helps ?!?

Discontinuities aren't a problem except that unwrap() sometimes fails.
Why do you need frequency at all? What are you doing?

Jerry
-- 
Engineering is the art of making what you want from things you can get.

On Oct 25, 11:30&#4294967295;am, Jerry Avins <j...@ieee.org> wrote:
> On 10/25/2011 11:02 AM, joanna wrote:
>
> > I think there are no phase discontinuities. I compute the phase in matlab
> > with this:
>
> > phase = unwrap(angle(z));
>
> > z is the analytic signal. unwrap corrects phase angles to produce smoother
> > phase plots. I dont't know if that means that i dont't have phase
> > discontinuities. My know-how in signal prosessing isn't so big :-)
>
> > I hope this answear helps ?!?
>
> Discontinuities aren't a problem except that unwrap() sometimes fails.
> Why do you need frequency at all? What are you doing?
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.

Hi Jerry,
How is everything is going well. I don't know if you are familiar with
EMD, so forgive this if you are. EMD is relatively recent analysis
method for non-linear and non-stationary signals. A "bunch" of guys
from NASA, NOAA, Naval Research Labs, Naval Surface Warfare, and NC
State wrote a paper on it for theRoyal Society around 1999 or 2000. It
breaks things down into "intrinic mode functions". With the Hilbert
transform the final thing you get is an energy/frequency/time
distribution. It looks at signals as basin intrinic mode oscillations
and gives instantaneous frequency as a function of time. Thus the need
to look at frequency.

That's about all I know about it - enough to be VERY dangerous :)

Joanna,
Is this is what you are studying? Are you using the Royal Society
paper as a basis? If so, maybe you can explain the concept behind the
Hilbert Spectrum.


Maurice Givens

On 10/25/2011 3:34 PM, maury wrote:

   ...

> Hi Jerry,
> How is everything is going well. I don't know if you are familiar with
> EMD, so forgive this if you are. EMD is relatively recent analysis
> method for non-linear and non-stationary signals. A "bunch" of guys
> from NASA, NOAA, Naval Research Labs, Naval Surface Warfare, and NC
> State wrote a paper on it for theRoyal Society around 1999 or 2000. It
> breaks things down into "intrinic mode functions". With the Hilbert
> transform the final thing you get is an energy/frequency/time
> distribution. It looks at signals as basin intrinic mode oscillations
> and gives instantaneous frequency as a function of time. Thus the need
> to look at frequency.
>
> That's about all I know about it - enough to be VERY dangerous :)
>
> Joanna,
> Is this is what you are studying? Are you using the Royal Society
> paper as a basis? If so, maybe you can explain the concept behind the
> Hilbert Spectrum.

Hi Maury,

Thanks for asking. I'm fine as long as I get regular maintenance. (Today 
I arrived at my dentist's at 1:30, had two teeth drilled and filled, and 
was back in my car at 2:00. Ain't modern times wonderful?) I hope you're 
well too.

Joanna's task, as I understand it, is identifying extrema in a set of 
data points in the presence of noise. I once attacked a similar problem 
by low-pass filtering the data to emphasize long-term trends. (My 
filter's coefficients were read off Pascal's triangle, my own invention 
and the only kind I knew how to calculate that was better than a boxcar 
averager. It is a convolution of N two-element averagers. and convinced 
me that I had better learn something about DSP.) FIR filters introduce 
known delay and corrupt the ends of the data points. My result was 
displayed as a graph of the original (unfiltered) data with vertical 
lines showing the extrema. Fortunately, I could ignore the ends, and 
dealt with the delay by subtracting the filter's phase delay.

I wouldn't be comfortable with this for all data and all uses, but it 
worked well enough for me. (The data were collected by, operated on, and 
displayed on a Nicolet oscilloscope.) Joanna wrote that she had done 
essentially the same thing, so I wondered how frequency came in. I know 
nothing of EMD, so I ignored the subject line of the thread. Bad!

Jerry
-- 
Engineering is the art of making what you want from things you can get.

On Oct 25, 3:15&#4294967295;pm, Jerry Avins <j...@ieee.org> wrote:
> On 10/25/2011 3:34 PM, maury wrote:
>
> &#4294967295; &#4294967295;...
>
>
>
>
>
> > Hi Jerry,
> > How is everything is going well. I don't know if you are familiar with
> > EMD, so forgive this if you are. EMD is relatively recent analysis
> > method for non-linear and non-stationary signals. A "bunch" of guys
> > from NASA, NOAA, Naval Research Labs, Naval Surface Warfare, and NC
> > State wrote a paper on it for theRoyal Society around 1999 or 2000. It
> > breaks things down into "intrinic mode functions". With the Hilbert
> > transform the final thing you get is an energy/frequency/time
> > distribution. It looks at signals as basin intrinic mode oscillations
> > and gives instantaneous frequency as a function of time. Thus the need
> > to look at frequency.
>
> > That's about all I know about it - enough to be VERY dangerous :)
>
> > Joanna,
> > Is this is what you are studying? Are you using the Royal Society
> > paper as a basis? If so, maybe you can explain the concept behind the
> > Hilbert Spectrum.
>
> Hi Maury,
>
> Thanks for asking. I'm fine as long as I get regular maintenance. (Today
> I arrived at my dentist's at 1:30, had two teeth drilled and filled, and
> was back in my car at 2:00. Ain't modern times wonderful?) I hope you're
> well too.
>
> Joanna's task, as I understand it, is identifying extrema in a set of
> data points in the presence of noise. I once attacked a similar problem
> by low-pass filtering the data to emphasize long-term trends. (My
> filter's coefficients were read off Pascal's triangle, my own invention
> and the only kind I knew how to calculate that was better than a boxcar
> averager. It is a convolution of N two-element averagers. and convinced
> me that I had better learn something about DSP.) FIR filters introduce
> known delay and corrupt the ends of the data points. My result was
> displayed as a graph of the original (unfiltered) data with vertical
> lines showing the extrema. Fortunately, I could ignore the ends, and
> dealt with the delay by subtracting the filter's phase delay.
>
> I wouldn't be comfortable with this for all data and all uses, but it
> worked well enough for me. (The data were collected by, operated on, and
> displayed on a Nicolet oscilloscope.) Joanna wrote that she had done
> essentially the same thing, so I wondered how frequency came in. I know
> nothing of EMD, so I ignored the subject line of the thread. Bad!
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.- Hide quoted text -
>
> - Show quoted text

Jerry,
I'm doing well too. The way I understand it (and this is very
simplistic), she needs to find all the positive peaks, then
essentially connect them to form a type of low-pass filter. Then do
the same for the negative peaks. Them the two are subtracted (called
the intrinic mode function IMF) to get the residule. The process is
then repeated for the residule. Each iteration gives an IMF (IMF0,
IMF1, ...).

Johanna,
Is this correct?

Maurice

On Oct 25, 1:15&#4294967295;pm, Jerry Avins <j...@ieee.org> wrote:
...
> I know
> nothing of EMD, so I ignored the subject line of the thread. Bad!
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.

For those with any interest, the royal Proceedings paper is available
at:
http://webber.physik.uni-freiburg.de/~jeti/studenten_seminar/stud_sem_WS_08_09/Huang_etal98.pdf

The title is:
The empirical mode decomposition and the
Hilbert spectrum for nonlinear and
non-stationary time series analysis
By  Norden  E.  Huang et al.

The empirical modes decompose a complex signal into components for
which the instantaneous frequency can be calculated. The empirical
modes do not rely on the properties of conventional transform basis
functions. YMMV.

Dale B. Dalrymple