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Rune Allnor wrote:
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:<DODeb.43$F...@feed2.centurytel.net>...
> 
>>"Rune Allnor" <a...@tele.ntnu.no> wrote in message
>>news:f...@posting.google.com...
>>
>>>Richard Owlett <r...@atlascomm.net> wrote in message
>>>
>>>>Do either of these problem definitions make sense to anyone but me?
>>>
>>>It does make sense to me. 
> 
> ....
> 
>>Rune,
>>
>>It doesn't make sense to me yet because I don't understand what some of the
>>operational steps are.
>>1) Feed white noise into 3 filters - OK
>>2) Filter outputs into a "perfect" amplifier - OK.
>>3) Gain (of the amplifier I guess) is a function of time - ?????  Why?  How?
>>4) The output of each amplifier is summed equally - I thought the objective
>>was to find the relative signal strength in the "bands" which I understood
>>to be "each band".  This implies the objective is to find the total signal
>>strength across all of the bands.  If so - OK.
>>5) "determine the gain of each of the amplifiers?  See (3).
>>
>>We've not talked about "linear superposition" even though it's mentioned in
>>the OP.  If the idea is to actually add the outputs of the filters as seems
>>to be implied above, then linear phase *and* of the same slope for each
>>filter is necessary methinks.  Otherwise, the composite will not be
>>representative of the spectral pieces of the input.
>>
>>Fred
> 
> 
> Fred, 
> 
> If I read the posts literally, I'll agree with you. However, I do, 
> for one reason or another, have the impression that the OP does not have 
> a very profound knowledge of the intricate subtleties of the various 
> aspects of DSP, including terminology, so I try to allow, rightly or 
> wrongly, for that.

OP says you are RIGHT ;!
I'm operating off memories of a 3rd year signals course I took 40 
years ago when attempting an EE degree. I've recently bought a house 
and getting a chance to bring things out of storage that haven't seen 
light of day in years. Found my signals text. Looking at table of 
contents, I suspect I'm confusing concepts which are 8 chapters apart 
in a 16 chapter book.

Thank you both for your time and patience.
Now off to work followed by 4 days off in a row.

>  
> If you go back to the first post, the analysis is not required to be 
> very sophisticated. I suspect that a filter bank consisting of relatively 
> simple low order IIR filters could help a lot. Only basic DSP knowledge 
> required, no fancy stuff involved, fast run-time etc. I read the post 
> basically as questions about implementations. 
> 
> Whether such crude analysis provides results that are useful in any way, 
> is a completely different issue that only the user can decide. Sure, 
> addressing power questions and signal reconstruction and so on is 
> difficult stuff, but these things do not appear to be very important.
> 
> Rune

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Richard Owlett <r...@atlascomm.net> wrote in message news:<v...@corp.supernews.com>...
> Rune Allnor wrote:
> 
> > [snip]> 
> > 
> > Sure. A Gabor plot, [snip]
> 
> Never heard of one so did Google search for "Gabor plot". Not much ;)
> But lead to searching "Gabor expansion" whose first hit was
> http://www.nari.ee.ethz.ch/commth/pubs/viewpub.php?ident=ms
> 
> In the abstract it stated:
> "... Gabor expansion, one of the major linear time-frequency signal 
> representations. The Gabor expansion, proposed by D. Gabor in 1946, is 
> the decomposition of a signal into a set of time-shifted and modulated 
> versions of an elementary window function."
> 
> Given that I do not actually have the foggiest notion of what it means:
> 
> It seems to "sort of" sound like what I might expect the description 
> of what I'm trying to do would appear in a thesis.
> 
> Can you point me to some elementary ( even simplistic ) description of 
> either  "Gabor plot" or "Gabor expansion" on the web?
> [One reference mentioned that in author's opinion not much was even 
> available in print.]

Sorry, can't help with references. I did this thing many years ago 
because that's what everybody else did, and I had a different approach 
to solve this particular problem. I had to demonstrate the properties 
of the Gabor plot in order to show that my plots were better...
I have a very vague recollection of having seen a paper that used the 
name "Gabor", but it's probably in the bottom of a 1.5 m high pile of 
articles.

The Gabor plots aren't a big deal: Take the signal and feed it into 
a number of parallel band-pass filters, e.g. a 1/3rd octave filter bank, 
square the samples in each output sequence (possibly use amplitude 
detectors instead) and plot the resulting time-frequency energy data as 
an image, contour plot or similar. This resulting plot is what I refer to 
as a "Gabor plot". It's not entirely dissimilar from a spectrogram, but 
computed in a different manner. 

The description of this "Gabor expansion" sounds like an early ancestor 
of the Wavelet Tranform. To me, wavelets are nothing but filter banks that 
have been optimized in certain respects. You may like to take a look on 
these thing as well. There may be people lurking out there who can point 
you to good sources.

Rune

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Richard Owlett wrote:

> Rune Allnor wrote:
>=20
>> [snip]>
>> Sure. A Gabor plot, [snip]
>=20
>=20
> Never heard of one so did Google search   ...

Don't you remember when Gabor -- he of hologram fame -- was suspected of =

a cabal to overthrow the Hungarian government? :-)

Jerry
--=20
Engineering is the art of making what you want from things you can get.
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

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Rune Allnor wrote:

   ...

>=20
> The description of this "Gabor expansion" sounds like an early ancestor=
=20
> of the Wavelet Tranform. To me, wavelets are nothing but filter banks t=
hat=20
> have been optimized in certain respects. You may like to take a look on=
=20
> these thing as well. There may be people lurking out there who can poin=
t=20
> you to good sources.
>=20
> Rune

Richard,

Have a look at http://www.amara.com/current/wavelet.html when you have ti=
me.

Jerry
--=20
Engineering is the art of making what you want from things you can get.
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

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"Rune Allnor" <a...@tele.ntnu.no> wrote in message
news:f...@posting.google.com...
> "Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
news:<DODeb.43$F...@feed2.centurytel.net>...
> > "Rune Allnor" <a...@tele.ntnu.no> wrote in message
> > news:f...@posting.google.com...
> > > Richard Owlett <r...@atlascomm.net> wrote in message
> > > > Do either of these problem definitions make sense to anyone but me?
> > >
> > > It does make sense to me.
> ...
> > Rune,
> >
> > It doesn't make sense to me yet because I don't understand what some of
the
> > operational steps are.
> > 1) Feed white noise into 3 filters - OK
> > 2) Filter outputs into a "perfect" amplifier - OK.
> > 3) Gain (of the amplifier I guess) is a function of time - ?????  Why?
How?
> > 4) The output of each amplifier is summed equally - I thought the
objective
> > was to find the relative signal strength in the "bands" which I
understood
> > to be "each band".  This implies the objective is to find the total
signal
> > strength across all of the bands.  If so - OK.
> > 5) "determine the gain of each of the amplifiers?  See (3).
> >
> > We've not talked about "linear superposition" even though it's mentioned
in
> > the OP.  If the idea is to actually add the outputs of the filters as
seems
> > to be implied above, then linear phase *and* of the same slope for each
> > filter is necessary methinks.  Otherwise, the composite will not be
> > representative of the spectral pieces of the input.
> >
> > Fred
>
> Fred,
>
> If I read the posts literally, I'll agree with you. However, I do,
> for one reason or another, have the impression that the OP does not have
> a very profound knowledge of the intricate subtleties of the various
> aspects of DSP, including terminology, so I try to allow, rightly or
> wrongly, for that.
>
> If you go back to the first post, the analysis is not required to be
> very sophisticated. I suspect that a filter bank consisting of relatively
> simple low order IIR filters could help a lot. Only basic DSP knowledge
> required, no fancy stuff involved, fast run-time etc. I read the post
> basically as questions about implementations.
>
> Whether such crude analysis provides results that are useful in any way,
> is a completely different issue that only the user can decide. Sure,
> addressing power questions and signal reconstruction and so on is
> difficult stuff, but these things do not appear to be very important.
>
> Rune

Rune,

OK - well now I understand from Richard that he wants to figure out the gain
of the "amplifiers" in the model.  Looks like a channel attenuation estimate
doesn't it?  That's much easier for me to understand now.

So, here's an answer:

1) Since this is a model, you want to know that the model itself is
reasonably representative of the system you're dealing with.  So, the first
question going in this direction would be:
Is a broadband noise input model with constant amplitude (I mean spectral
density such as volts per Hz or volts per sqrt Hz type of measure) a
reasonable model for the situation?
I can see that you might lump the signal source strength into the amplifier
gain - so that could be OK as long as you're aware of it and can accept it.
Otherwise, there will be no way to separate out signal strength vs. channel
gain/attenuation.

2) Ditto for the bandwidth of the filters.  Does the bandwidth stay fairly
constant at the output in what you're trying to model?  Maybe overkill to
consider in your situation ......

If these two things are OK, then a measure of the energy out of the
amplifiers as a function of time should give you an estimate of the gain of
the model's amplifiers - given that you are willing to state the input
amplitude ahead of time or simply want to know relative gain from one time
to another time.  Sum of the squared values of the output may do or the sqrt
of same is perhaps more appropriate.

The only thing left to say is that you should integrate / sum the energy
over a time period that is somewhat long compared to the reciprocal of the
bandwidth of the filter in each case or long compared to the reciprocal of
the bandwidth of the narrowest filter if all the measures need to be the
same or done in parallel.  Otherwise, if the measurement time is too short,
the outputs will vary quite a bit and you'll be looking at "source"
variations instead of a reasonable average - the latter is what you want.
It's the difference between observing the noise wiggling around and
observing slower changes in the "amplifier".  If the "amplifier" gain is
supposed to change as fast or faster than the input then you might want to
reassess the model you'll be using.

Fred

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Jerry Avins wrote:
> Rune Allnor wrote:
> 
>   ...
> 
>>
>> The description of this "Gabor expansion" sounds like an early 
>> ancestor of the Wavelet Tranform. To me, wavelets are nothing but 
>> filter banks that have been optimized in certain respects. You may 
>> like to take a look on these thing as well. There may be people 
>> lurking out there who can point you to good sources.
>>
>> Rune
> 
> 
> Richard,
> 
> Have a look at http://www.amara.com/current/wavelet.html when you have 
> time.
> 
> Jerry


I see why the qualification "when you have time ";}
Thanks.

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a...@tele.ntnu.no (Rune Allnor) wrote in message news:<f...@posting.google.com>...
> The Gabor plots aren't a big deal: Take the signal and feed it into 
> a number of parallel band-pass filters, e.g. a 1/3rd octave filter bank, 
> square the samples in each output sequence (possibly use amplitude 
> detectors instead) 

Make that "envelope detector", not "amplitude detector"...

> and plot the resulting time-frequency energy data as 
> an image, contour plot or similar. This resulting plot is what I refer to 
> as a "Gabor plot". It's not entirely dissimilar from a spectrogram, but 
> computed in a different manner. 

Rune

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Rune Allnor wrote:

> [snip]
> 
> The Gabor plots aren't a big deal: Take the signal and feed it into 
> a number of parallel band-pass filters, e.g. a 1/3rd octave filter bank, 
> square the samples in each output sequence (possibly use amplitude 
> detectors instead) and plot the resulting time-frequency energy data as 
> an image, contour plot or similar. This resulting plot is what I refer to 
> as a "Gabor plot". It's not entirely dissimilar from a spectrogram, but 
> computed in a different manner. 
> 

That sounds like a high octane version of what I was groping towards.
[ There are regions where decade would be appropriate. On occasion 
decade would be too wide. Third octave would always be unnessasarily 
narrow. ]

However, since the underlying assumption I wish to test PRESUMES that 
the signal is "pink" in region of interest, 1/3 octave filters might 
be wide enough to ensure "pink-ness" and narrow enough to reduce 
computational load.

I need to look at links from Jerry's reference before going too much 
further. The summarry of a couple of the links indicated that they 
touched on what kind of analysis would be appropriate for what kind of 
problem.

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Fred Marshall wrote:

> "Rune Allnor" <a...@tele.ntnu.no> wrote in message
> news:f...@posting.google.com...
> 
>>"Fred Marshall" <fmarshallx@remove_the_x.acm.org> wrote in message
> 
> news:<DODeb.43$F...@feed2.centurytel.net>...
> 
>>>"Rune Allnor" <a...@tele.ntnu.no> wrote in message
>>>news:f...@posting.google.com...
>>>
>>>>Richard Owlett <r...@atlascomm.net> wrote in message
>>>>
>>>>>Do either of these problem definitions make sense to anyone but me?
>>>>
>>>>It does make sense to me.
>>
>>...
>>
>>>Rune,
>>>
>>>It doesn't make sense to me yet because I don't understand what some of
> 
> the
> 
>>>operational steps are.
>>>1) Feed white noise into 3 filters - OK
>>>2) Filter outputs into a "perfect" amplifier - OK.
>>>3) Gain (of the amplifier I guess) is a function of time - ?????  Why?
> 
> How?
> 
>>>4) The output of each amplifier is summed equally - I thought the
> 
> objective
> 
>>>was to find the relative signal strength in the "bands" which I
> 
> understood
> 
>>>to be "each band".  This implies the objective is to find the total
> 
> signal
> 
>>>strength across all of the bands.  If so - OK.
>>>5) "determine the gain of each of the amplifiers?  See (3).
>>>
>>>We've not talked about "linear superposition" even though it's mentioned
> 
> in
> 
>>>the OP.  If the idea is to actually add the outputs of the filters as
> 
> seems
> 
>>>to be implied above, then linear phase *and* of the same slope for each
>>>filter is necessary methinks.  Otherwise, the composite will not be
>>>representative of the spectral pieces of the input.
>>>
>>>Fred
>>
>>Fred,
>>
>>If I read the posts literally, I'll agree with you. However, I do,
>>for one reason or another, have the impression that the OP does not have
>>a very profound knowledge of the intricate subtleties of the various
>>aspects of DSP, including terminology, so I try to allow, rightly or
>>wrongly, for that.
>>
>>If you go back to the first post, the analysis is not required to be
>>very sophisticated. I suspect that a filter bank consisting of relatively
>>simple low order IIR filters could help a lot. Only basic DSP knowledge
>>required, no fancy stuff involved, fast run-time etc. I read the post
>>basically as questions about implementations.
>>
>>Whether such crude analysis provides results that are useful in any way,
>>is a completely different issue that only the user can decide. Sure,
>>addressing power questions and signal reconstruction and so on is
>>difficult stuff, but these things do not appear to be very important.
>>
>>Rune
> 
> 
> Rune,
> 
> OK - well now I understand from Richard that he wants to figure out the gain
> of the "amplifiers" in the model.  Looks like a channel attenuation estimate
> doesn't it?  That's much easier for me to understand now.
> 
> So, here's an answer:
> 
> 1) Since this is a model, you want to know that the model itself is
> reasonably representative of the system you're dealing with.  So, the first
> question going in this direction would be:
> Is a broadband noise input model with constant amplitude (I mean spectral
> density such as volts per Hz or volts per sqrt Hz type of measure) a
> reasonable model for the situation?

Actually that is EXPLICITLY one of the questions I'm trying to answer 
experimentally.

> I can see that you might lump the signal source strength into the amplifier
> gain - so that could be OK as long as you're aware of it and can accept it.
> Otherwise, there will be no way to separate out signal strength vs. channel
> gain/attenuation.

My description is at fault here.
In these terms the variable of interest would be the {strength gain 
product). I was looking for a description that would intropduce as 
feww red herrings as possible -- may not have succeeded.

> 
> 2) Ditto for the bandwidth of the filters.  Does the bandwidth stay fairly
> constant at the output in what you're trying to model?  Maybe overkill to
> consider in your situation ......
> 
> If these two things are OK, then a measure of the energy out of the
> amplifiers as a function of time should give you an estimate of the gain of
> the model's amplifiers - given that you are willing to state the input
> amplitude ahead of time or simply want to know relative gain from one time
> to another time.  Sum of the squared values of the output may do or the sqrt
> of same is perhaps more appropriate.


Actually I was describing one possible set of contents of "black box" 
to which I only had access to ONE 'output' node.


> 
> The only thing left to say is that you should integrate / sum the energy
> over a time period that is somewhat long compared to the reciprocal of the
> bandwidth of the filter in each case or long compared to the reciprocal of
> the bandwidth of the narrowest filter if all the measures need to be the
> same or done in parallel.  

I think that can be satisfied. ( 1/[frame rate] will be less that .5 
lowest freq of interest and would tend towards at least octave 
separation ( on ocassion decades)).



> Otherwise, if the measurement time is too short,
> the outputs will vary quite a bit and you'll be looking at "source"
> variations instead of a reasonable average - the latter is what you want.
> It's the difference between observing the noise wiggling around and
> observing slower changes in the "amplifier".  If the "amplifier" gain is
> supposed to change as fast or faster than the input then you might want to
> reassess the model you'll be using.
> 
> Fred
> 
> 

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Richard Owlett <r...@atlascomm.net> wrote in message news:<v...@corp.supernews.com>...
> OP says you are RIGHT ;!

Sorry 'bout that one... I'll make an effort *not* to discuss somebody 
in 3rd person in public henceforth...

Rune

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