Concatenating Data

Dear Group,

I have a time series consisting of vibration data that posseses multiple
periods in which there is very little vibration activity. I want to
eliminate these segments and join the segments of the time series that
contain vibration activity so that I am still left with one (but shorter)
time series. The questions I have regarding this procedure is  twofold:

1. What is the technical name for this procedure.
2. How can this be done (if at all) without introducing additional frequency
componenets.

Best Regards,

Luca

Luca Notini wrote:


> I have a time series consisting of vibration data that posseses multiple
> periods in which there is very little vibration activity. I want to
> eliminate these segments and join the segments of the time series that
> contain vibration activity so that I am still left with one (but shorter)
> time series. The questions I have regarding this procedure is  twofold:

> 1. What is the technical name for this procedure.

Maybe it doesn't have one.  How about concatenating unrelated
time series?

> 2. How can this be done (if at all) without introducing
> additional frequency componenets.

It depends very much on what you are trying to do.  If they really
are separate, I would take them as separate time series and analyze
each one on its own.

As for frequency components, say you have a signal with 67.1Hz and 
67.2Hz frequency components of constant amplitude.  You might then
describe it as a case where the vibration goes away for five
seconds every ten seconds.   (With more components one can arrange
different amplitude patterns, even though each component is constant
in amplitude.)

Is the difference between 67.1 and 67.2 important to you?

If you take two time series from the signal described, you will
likely get two other frequencies near 67.15Hz.

One thing is that the length of a time series should be at least
twice as long as the reciprocal of the frequency resolution you want.
(I think it is twice.  There is a factor of two that is easy to get 
wrong.)  Concatenating individual time series adds interference
terms which should not be there.

-- glen

Luca Notini wrote:
> Dear Group,
> 
> I have a time series consisting of vibration data that posseses multiple
> periods in which there is very little vibration activity. I want to
> eliminate these segments and join the segments of the time series that
> contain vibration activity so that I am still left with one (but shorter)
> time series. The questions I have regarding this procedure is  twofold:
> 
> 1. What is the technical name for this procedure.

Garbage in, garbage out.

> 2. How can this be done (if at all) without introducing additional frequency
> componenets.

Congratulations, you see at least part of the problem.

A man known for frugality and strong family ties went to the doctor's
office to get the results of a urinalysis and brought his family with
him. On hearing the good news that there was no sign of disease, he
turned to his family and said, "Congratulations! We're all healthy."

It might be useful to average the amplitude information in individual
FFTs of the useful data series. Averaging the frequency data is not the
same as concatenating the time data.

Maybe I'm wrong. For your sake, I hope so. Get a second opinion.

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

Luca Notini wrote:

> Dear Group,
> 
> I have a time series consisting of vibration data that posseses multiple
> periods in which there is very little vibration activity. I want to
> eliminate these segments and join the segments of the time series that
> contain vibration activity so that I am still left with one (but shorter)
> time series. The questions I have regarding this procedure is  twofold:
> 
> 1. What is the technical name for this procedure.
> 2. How can this be done (if at all) without introducing additional frequency
> componenets.
> 
> Best Regards,
> 
> Luca
> 
> 

As pointed out by OP, this may not be the world's best way to get where 
you want to go.

If you have (effectively) a number of different samples that you want to 
combine into one answer I would suggest taking the power spectral 
density of each section, then average the PSDs (_not_ the actual FFT 
coefficients -- use the power).

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tim Wescott wrote:
> Luca Notini wrote:
> 
>> Dear Group,
>>
>> I have a time series consisting of vibration data that posseses multiple
>> periods in which there is very little vibration activity. I want to
>> eliminate these segments and join the segments of the time series that
>> contain vibration activity so that I am still left with one (but shorter)
>> time series. The questions I have regarding this procedure is  twofold:
>>
>> 1. What is the technical name for this procedure.
>> 2. How can this be done (if at all) without introducing additional 
>> frequency
>> componenets.
>>
>> Best Regards,
>>
>> Luca
>>
>>
> 
> As pointed out by OP, this may not be the world's best way to get where 
> you want to go.
> 
> If you have (effectively) a number of different samples that you want to 
> combine into one answer I would suggest taking the power spectral 
> density of each section, then average the PSDs (_not_ the actual FFT 
> coefficients -- use the power).

Unless there is reason to weight the average toward those runs with
higher amplitude, averaging amplitude may give a more revealing plot.
Power is merely the square of amplitude, to the extra effort is only a
square root per bin.

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

"Jerry Avins" <jya@ieee.org> wrote in message
news:4084455e$0$16484$61fed72c@news.rcn.com...
> Tim Wescott wrote:
> > Luca Notini wrote:
> >
> >> I have a time series consisting of vibration data that posseses
multiple
> >> periods in which there is very little vibration activity. I want to
> >> eliminate these segments and join the segments of the time series that
> >> contain vibration activity so that I am still left with one (but
shorter)
> >> time series. The questions I have regarding this procedure is  twofold:
> >>
> >> 1. What is the technical name for this procedure.
> >> 2. How can this be done (if at all) without introducing additional
> >> frequency
> >> componenets.

> > If you have (effectively) a number of different samples that you want to
> > combine into one answer I would suggest taking the power spectral
> > density of each section, then average the PSDs (_not_ the actual FFT
> > coefficients -- use the power).
>
> Unless there is reason to weight the average toward those runs with
> higher amplitude, averaging amplitude may give a more revealing plot.
> Power is merely the square of amplitude, to the extra effort is only a
> square root per bin.

Usually the power is averaged, I believe because this is more meaningful and
more directly useful when looking at noise and vibrations, and also because
it's faster to not do the square root.  After averaging, you may or may not
want to do a square root to back to an RMS level.

-- 
Eric Backus

Jerry Avins wrote:

> Tim Wescott wrote:
> 
>> Luca Notini wrote:
>>
>>> Dear Group,
>>>
>>> I have a time series consisting of vibration data that posseses multiple
>>> periods in which there is very little vibration activity. I want to
>>> eliminate these segments and join the segments of the time series that
>>> contain vibration activity so that I am still left with one (but 
>>> shorter)
>>> time series. The questions I have regarding this procedure is  twofold:
>>>
>>> 1. What is the technical name for this procedure.
>>> 2. How can this be done (if at all) without introducing additional 
>>> frequency
>>> componenets.
>>>
>>> Best Regards,
>>>
>>> Luca
>>>
>>>
>>
>> As pointed out by OP, this may not be the world's best way to get 
>> where you want to go.
>>
>> If you have (effectively) a number of different samples that you want 
>> to combine into one answer I would suggest taking the power spectral 
>> density of each section, then average the PSDs (_not_ the actual FFT 
>> coefficients -- use the power).
> 
> 
> Unless there is reason to weight the average toward those runs with
> higher amplitude, averaging amplitude may give a more revealing plot.
> Power is merely the square of amplitude, to the extra effort is only a
> square root per bin.
> 

Do you mean averaging the complex coefficients, or averaging the 
absolute value of the amplitude?  Averaging the complex coefficients 
would cause problems because the data is incoherent which renders the 
relative phase between samples essentially random.  For a small number 
of segments this would enhance, rather than decrease, the variation of 
the result.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

"Luca Notini" <l.notini2@lboro.ac.uk> wrote in message news:<c61687$slt$1@sun-cc204.lut.ac.uk>...
> Dear Group,
> 
> I have a time series consisting of vibration data that posseses multiple
> periods in which there is very little vibration activity. I want to
> eliminate these segments and join the segments of the time series that
> contain vibration activity so that I am still left with one (but shorter)
> time series. The questions I have regarding this procedure is  twofold:
> 
> 1. What is the technical name for this procedure.
> 2. How can this be done (if at all) without introducing additional frequency
> componenets.
> 
> Best Regards,
> 
> Luca

You should be very careful. As others have already said, you might want 
to view each segment as a separate time series. Initial transients may 
be different, if you concatenate the data in the "wrong" way you might 
introduce phase jumps and end up with a spread spectrum type of signal, 
there are just too much that can go wrong here. 

It may be possible to give better advice if you post a description of the 
measurements you do and indicate what you are looking for in the data.

Rune

You could reduce the spectrum spreading effect caused by sample start/end
discontinuities by windowing (tapering) the leading and trailing edges of
each sample data file.  The time duration of the sample files will need to
be significantly longer than that of the lowest frequency of interest.

A lot depends on just what you are trying to achieve.  In this case I assume
you are summarising data.  You could window each file and just add the
corresponding samples of each file if they are of similar length.

Jim A.

Tim Wescott wrote:

> Jerry Avins wrote:

   ...

>> Unless there is reason to weight the average toward those runs with
>> higher amplitude, averaging amplitude may give a more revealing plot.
>> Power is merely the square of amplitude, to the extra effort is only a
>> square root per bin.
>>
> 
> Do you mean averaging the complex coefficients, or averaging the 
> absolute value of the amplitude?  Averaging the complex coefficients 
> would cause problems because the data is incoherent which renders the 
> relative phase between samples essentially random.  For a small number 
> of segments this would enhance, rather than decrease, the variation of 
> the result.

I meant the amplitude. Depending on context, averaging power (= a^2+b^2;
sample = a+jb), taking the square root of that (= RMS), or amplitude {=
sqrt(a^2+b^2)} may be most revealing. One can expect any of these
measures to represent the system giving rise to them regardless of any
delays. Phase, as you point out indirectly, can vary widely and must be
ignored. Amplitude and power ignore it.

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