| Author |
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Jon Harris
Guest
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 Posted:
Mon Dec 13, 2004 11:48 pm Post subject:
Re: Struggling with waveform questions. |
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"Stan Pawlukiewicz" <spam@spam.mitre.org> wrote in message
news:cpkb67$qlt$1@newslocal.mitre.org...
| Quote: | Stephan M. Bernsee wrote:
On 2004-12-13 00:52:51 +0100, "Fred Marshall"
fmarshallx@remove_the_x.acm.org> said:
***The zeroeth harmonic doesn't have phase. The first harmonic does
though.... and establishes where time=0 must be relative to the first
harmonic and, thereby, the others.
The first harmonic is the fundamental (= the zeroth overtone). It does
have a phase, as does the zeroth harmonic (DC) itself. It's just that
for DC phase is a constant because it has zero frequency...
My understanding is that frequencies below the fundamental are called
sub harmonics. I interpret the zeroth harmonic to be the fundamental.
In the sort of applications I deal with, DC doesn't propagate, so I've
never thought of it as a harmonic.
|
One way in which the numbering of harmonics make mathematical sense is if you
say the "nth" harmonic represents the fundamental frequency times n. In that
case, fundamental = 1st harmonic. |
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Stan Pawlukiewicz
Guest
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| Posted:
Mon Dec 13, 2004 11:57 pm Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins wrote:
| Quote: | Stan Pawlukiewicz wrote:
... I interpret the zeroth harmonic to be the fundamental. ...
So how do you interpret "first harmonic"? If I have a crystal whose
fundamental is 9 MHz and is marked "third overtone", at what frequency
do you expect it to be used?
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When in doubt I look at the spec sheet and try to figure what make sense.
| Quote: |
We are discussing at excessive length definitions that can be looked up,
which makes no more sense than voting to decide what time it is.
|
Not trying to be a smart ass, but standardized time zones didn't spring
forth from the brow of Jov, it took an act of congress to adopt them.
A few years ago I visited the US Naval Observatory on a tour and viewed
the official US time standard. The official time of the United Sates is
the average of 256 atomic clocks.
Quoting
| Quote: | from http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html:
"The lowest resonant frequency of a vibrating object is
called its fundamental frequency. Most vibrating objects
have more than one resonant frequency and those used in
musical instruments typically vibrate at harmonics of the
fundamental. A harmonic is defined as an integer (whole
number) multiple of the fundamental frequency."
|
If I recall correctly, the resonant frequencies of a drum are related to
the zeros of the Bessel Function, not simple integer multiples.
In shaft driven machinery where there is slippage and dynamics, the
harmonics are not necessarily related by integers.
I think that the above definition is inadequate.
| Quote: |
According to that, if the fundamental frequency is F, the frequencies
defined by the integers 0, 1, and 2 are DC, F, and 2F.
|
By that convention DC is the fundamental of everything which make me
distrust the above definition even more.
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Stan Pawlukiewicz
Guest
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| Posted:
Mon Dec 13, 2004 11:58 pm Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins wrote:
| Quote: | Stan Pawlukiewicz wrote:
...
I don't like the notion of DC being a harmonic. It would be a harmonic
of all signals.
It is. Zero has some funny properties.
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I'm not laughing.
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Randy Yates
Guest
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| Posted:
Tue Dec 14, 2004 12:09 am Post subject:
Re: Struggling with waveform questions. |
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Richard Dobson <richarddobson@blueyonder.co.uk> writes:
Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124 |
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Stan Pawlukiewicz
Guest
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| Posted:
Tue Dec 14, 2004 12:10 am Post subject:
Re: Struggling with waveform questions. |
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Jon Harris wrote:
| Quote: | "Stan Pawlukiewicz" <spam@spam.mitre.org> wrote in message
news:cpkb67$qlt$1@newslocal.mitre.org...
Stephan M. Bernsee wrote:
On 2004-12-13 00:52:51 +0100, "Fred Marshall"
fmarshallx@remove_the_x.acm.org> said:
***The zeroeth harmonic doesn't have phase. The first harmonic does
though.... and establishes where time=0 must be relative to the first
harmonic and, thereby, the others.
The first harmonic is the fundamental (= the zeroth overtone). It does
have a phase, as does the zeroth harmonic (DC) itself. It's just that
for DC phase is a constant because it has zero frequency...
My understanding is that frequencies below the fundamental are called
sub harmonics. I interpret the zeroth harmonic to be the fundamental.
In the sort of applications I deal with, DC doesn't propagate, so I've
never thought of it as a harmonic.
One way in which the numbering of harmonics make mathematical sense is if you
say the "nth" harmonic represents the fundamental frequency times n. In that
case, fundamental = 1st harmonic.
It really only makes sense for strings. I've heard the term zeroth mode |
applied to the evanvesant mode of a wave guide. |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 12:15 am Post subject:
Re: Struggling with waveform questions. |
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Randy Yates wrote:
| Quote: | Jerry Avins <jya@ieee.org> writes:
Randy Yates wrote:
Jerry Avins <jya@ieee.org> writes:
Randy Yates wrote:
...
Have you added any information to the topic? It seems to me you've just
confirmed that "this terminology has come to be used in this manner in
the field." The distinction between "harmonic" and "element of a set of
harmonics" is nil.
I'm made the case that "first harmonic" is a synonym for "fundamental",
Whether or not it's a synonym depends on how it's defined. According
to Webster, it is NOT a synonym. Do you disagree?
The definition in Webster if fine in its context. I disagree in the
context of engineering.
That was what my first post on subject said. I'm not disagreeing with
the usage in the context of engineering, just stating that it is at
odds with the colloquial use of the term.
|
Good! Please overlook my obtuseness.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 12:31 am Post subject:
Re: Struggling with waveform questions. |
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Stan Pawlukiewicz wrote:
| Quote: | Jerry Avins wrote:
Stan Pawlukiewicz wrote:
... I interpret the zeroth harmonic to be the fundamental. ...
So how do you interpret "first harmonic"? If I have a crystal whose
fundamental is 9 MHz and is marked "third overtone", at what frequency
do you expect it to be used?
When in doubt I look at the spec sheet and try to figure what make sense.
|
That's a weasel. It's meant to oscillate at its third overtone, about 27
MHz. On the other hand, if it's run at its fundamental and fed into a
push-push tripler, it will produce exactly 27 MHz, it's third harmonic.
| Quote: | We are discussing at excessive length definitions that can be looked up,
which makes no more sense than voting to decide what time it is.
Not trying to be a smart ass, but standardized time zones didn't spring
forth from the brow of Jov, it took an act of congress to adopt them.
|
Solar time is properly determined by observation, not majority opinion.
| Quote: | A few years ago I visited the US Naval Observatory on a tour and viewed
the official US time standard. The official time of the United Sates is
the average of 256 atomic clocks.
|
Those clocks are in turn set by observation, not consensus.
| Quote: | Quoting
from http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html:
"The lowest resonant frequency of a vibrating object is
called its fundamental frequency. Most vibrating objects
have more than one resonant frequency and those used in
musical instruments typically vibrate at harmonics of the
fundamental. A harmonic is defined as an integer (whole
number) multiple of the fundamental frequency."
If I recall correctly, the resonant frequencies of a drum are related to
the zeros of the Bessel Function, not simple integer multiples.
|
I believe that's correct. We agree that not all overtones are even
approximately harmonic. What we're discussing (I thought) is the
appropriate numbering of harmonics.
| Quote: | In shaft driven machinery where there is slippage and dynamics, the
harmonics are not necessarily related by integers.
|
Harmonics are always related by integers. You need to distinguish
between harmonics and more general overtones.
| Quote: | I think that the above definition is inadequate.
|
Properly used, they serve nicely.
...
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Stan Pawlukiewicz
Guest
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| Posted:
Tue Dec 14, 2004 12:57 am Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins wrote:
| Quote: | Stan Pawlukiewicz wrote:
Jerry Avins wrote:
Stan Pawlukiewicz wrote:
... I interpret the zeroth harmonic to be the fundamental. ...
So how do you interpret "first harmonic"? If I have a crystal whose
fundamental is 9 MHz and is marked "third overtone", at what frequency
do you expect it to be used?
When in doubt I look at the spec sheet and try to figure what make sense.
That's a weasel. It's meant to oscillate at its third overtone, about 27
MHz. On the other hand, if it's run at its fundamental and fed into a
push-push tripler, it will produce exactly 27 MHz, it's third harmonic.
|
I don't step in bear traps, if that make me a weasel then I'm a weasel.
| Quote: |
We are discussing at excessive length definitions that can be looked up,
which makes no more sense than voting to decide what time it is.
Not trying to be a smart ass, but standardized time zones didn't spring
forth from the brow of Jov, it took an act of congress to adopt them.
Solar time is properly determined by observation, not majority opinion.
Depends on where you stand.
A few years ago I visited the US Naval Observatory on a tour and viewed
the official US time standard. The official time of the United Sates is
the average of 256 atomic clocks.
Those clocks are in turn set by observation, not consensus.
|
The observatory is in Washington DC which isn't on any meridian. Some
body had to agree where the meridians where. Some body had to agree
what standard to use to set the standard.
| Quote: |
Quoting
from http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html:
"The lowest resonant frequency of a vibrating object is
called its fundamental frequency. Most vibrating objects
have more than one resonant frequency and those used in
musical instruments typically vibrate at harmonics of the
fundamental. A harmonic is defined as an integer (whole
number) multiple of the fundamental frequency."
If I recall correctly, the resonant frequencies of a drum are related to
the zeros of the Bessel Function, not simple integer multiples.
I believe that's correct. We agree that not all overtones are even
approximately harmonic. What we're discussing (I thought) is the
appropriate numbering of harmonics.
In shaft driven machinery where there is slippage and dynamics, the
harmonics are not necessarily related by integers.
Harmonics are always related by integers. You need to distinguish
between harmonics and more general overtones.
|
I have a friend who wrote his Master's thesis in EE on detecting
non-integer harmonics. The term "harmonic" has become a bit more
general. You can find IEEE articles that use the traditional usage and
others that talk about generalized harmonics.
| Quote: |
I think that the above definition is inadequate.
Properly used, they serve nicely.
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Traditions only serve the traditional.
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Jerry Avins
Guest
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| Posted:
Tue Dec 14, 2004 1:09 am Post subject:
Re: Struggling with waveform questions. |
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Randy Yates wrote:
| Quote: | Richard Dobson <richarddobson@blueyonder.co.uk> writes:
[...]
Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.
|
And never the twain shall communicate.
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Erik de Castro Lopo
Guest
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| Posted:
Tue Dec 14, 2004 1:10 am Post subject:
Re: Struggling with waveform questions. |
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"Stephan M. Bernsee" wrote:
| Quote: |
On 2004-12-13 00:52:51 +0100, "Fred Marshall"
fmarshallx@remove_the_x.acm.org> said:
***The zeroeth harmonic doesn't have phase. The first harmonic does
though.... and establishes where time=0 must be relative to the first
harmonic and, thereby, the others.
The first harmonic is the fundamental (= the zeroth overtone). It does
have a phase, as does the zeroth harmonic (DC) itself. It's just that
for DC phase is a constant because it has zero frequency...
|
If thats how you define the zeroth harmonic then I have to agree. As
far back as I can remember (high school maths about 25 years ago), the
zeroth harmonic was the fundamental.
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam@mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
"I have long argued that the entertainment industry doesn't want
people to have computers. Computers give users too much capability,
too much flexibility, too much freedom. The entertainment industry
wants users to sit back and consume things. They are trying to
turn a computer into an Internet Entertainment Platform, along the
lines of a television or VCR. This bill is a large step in that
direction." -- Bruce Schneier |
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glen herrmannsfeldt
Guest
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| Posted:
Tue Dec 14, 2004 1:12 am Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins wrote:
(snip on harmonics and crystals, not necessarily in that order)
| Quote: | That's a weasel. It's meant to oscillate at its third overtone, about 27
MHz. On the other hand, if it's run at its fundamental and fed into a
push-push tripler, it will produce exactly 27 MHz, it's third harmonic.
|
I don't believe this is true for crystals, though I haven't thought
about it in a while. It will be close, but not close enough for
some people. (Especially radio users with well defined frequencies.)
If you consider the modes of an air column in a tube, such as a
pipe organ of flute you will find that the higher modes are not exactly
integer multiples. For an air column there is an end effect due to the
finite diameter of the tube, such that the boundary condition doesn't
occur right at the physical end of the tube. For crystals, it might
be due to the effects of the plated electrodes on the crystal faces not
having the same physical properties as quartz. Probably close enough
for processor clocks, though.
(I once tried to get an intel 8284, clock generator for the 8087 to
run with a 24 MHz crystal. After some time I found it running about
about 7.5MHz and couldn't convince it to run at 24. I bought a 22MHz
crystal and it worked fine, though a little slower.)
-- glen |
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Jon Harris
Guest
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| Posted:
Tue Dec 14, 2004 1:18 am Post subject:
Re: Struggling with waveform questions. |
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"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpoegyj9rm.fsf@usrts005.corpusers.net...
| Quote: | Richard Dobson <richarddobson@blueyonder.co.uk> writes:
[...]
Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.
|
Without context it's hard to remember what "your" definition is, but in the
audio engineering business, the usage of the terms "even harmonics" and "odd
harmonics" is very common, especially when talking about distortion. Odd
harmonics are what a square wave has (e.g. 100 Hz square wave has components at
100, 300, 500, 700... Hz). I would think any definition used in the audio
engineering business should ensure that the odd numbered harmonics (1st, 3rd,
5th...) correspond to the odd harmonics. This pretty much requires that the
fundamental be the 1st harmonic. |
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glen herrmannsfeldt
Guest
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| Posted:
Tue Dec 14, 2004 1:25 am Post subject:
Re: Struggling with waveform questions. |
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Jon Harris wrote:
(big snip)
| Quote: | I'm with Jerry on this one. My music teacher (who is a musician, not an
engineer), used to emphasize that the 1st overtone is the 2nd harmonic, etc.
because the fundamental counts as an overtone.
|
I do agree that the first harmonic is the fundamental, but
overtones are a different question. I do know that crystal
oscillators come in overtones which are odd numbers, and that crystals
can only run at odd numbers, such that the voltage on the electrodes
is different.
http://www.circuitcellar.com/library/print/0298/bujanos91/11.htm
Which I guess I believe indicated that harmonics are multiples of the
fundaments. while overtones for a variety of physical reasons are not
exact multiples. This is true for music as well as quartz crystals.
There is an end effect such that the node or antinode is not exactly
at the end of the tube for a vibrating air column, for example. For
a string it is probably pretty close. For a quartz crystal it might be
the effect of the electrodes.
A third overtone crystal vibrates at approximately three times the
fundamental frequency, and is called third overtone not third harmonic.
-- glen |
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Stephan M. Bernsee
Guest
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| Posted:
Tue Dec 14, 2004 1:45 am Post subject:
Re: Struggling with waveform questions. |
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On 2004-12-13 16:06:41 +0100, Stan Pawlukiewicz <spam@spam.mitre.org> said:
| Quote: | Stephan M. Bernsee wrote:
On 2004-12-13 00:52:51 +0100, "Fred Marshall"
fmarshallx@remove_the_x.acm.org> said:
***The zeroeth harmonic doesn't have phase. The first harmonic does
though.... and establishes where time=0 must be relative to the first
harmonic and, thereby, the others.
The first harmonic is the fundamental (= the zeroth overtone). It does
have a phase, as does the zeroth harmonic (DC) itself. It's just that
for DC phase is a constant because it has zero frequency...
My understanding is that frequencies below the fundamental are called
sub harmonics. I interpret the zeroth harmonic to be the fundamental.
In the sort of applications I deal with, DC doesn't propagate, so I've
never thought of it as a harmonic.
|
The sub-harmonics usually appear at integer fractions of the frequency
of the first harmonic, so it's not at all a contradiction, just a
regular harmonic series :-)
The first sub-harmonic would appear at half the frequency of the first
harmonic, ie. one octave below it (= 1/2 f). IMHO that would be
consistent with the "fundamental" being the first harmonic (= 1/1 f),
but *not* if it were the zeroth harmonic!
So indeed your example of subharmonics is a counterexample of what you said.
There's another problem: in the realm of psychoacoustics, the
"fundamental" frequency (the "pitch" of a note) might not be the first
harmonic contained in a sound. Indeed, there are cases of sounds (in
speech for example) where energy at the fundamental frequency is
completely missing, so the first overtone (= second harmonic) would be
the first constituent frequency but *not* the fundamental.
Therefore, you can't just number them as they appear but you have to
evaluate the harmonic relationship as well if you really want to label
a frequency the "fundamental"...
I agree it's all a matter of convention and definition. From the
musical POV (where I come from) I have to agree with what Richard said
about the piano string. In fact, it's the exact same model I use in my
"DFT à Pied" article at http://dspdimension.com/img/sinemixl.jpg and
IMHO the only one that *really* explains this consistently.
--
Stephan M. Bernsee
http://www.dspdimension.com |
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Stephan M. Bernsee
Guest
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| Posted:
Tue Dec 14, 2004 1:55 am Post subject:
Re: Struggling with waveform questions. |
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On 2004-12-13 16:35:20 +0100, Jerry Avins <jya@ieee.org> said:
| Quote: | Frequency is the rate at which phase changes. That's a notion pretty
much inapplicable to DC. If one says that DC has constant phase, then
all instances of DC must have the same phase. What is it? Why did you
choose that one? It isn't reasonable to claim that 0, 6, and 12VDC are
really 12VDC at phase angles of 0, 30 and 90 degrees respectively. I
think it simplifies matters to take it that DC has no phase.
Jerry
|
Jerry, I beg you pardon if I quote you with "Zero has some funny
properties." Changing the numbers doesn't change the concept, IMHO, so
the concept of phase doesn't go away if the frequency approaches zero.
It's the same thing when you divide by zero - you could say the result
is infinity or argue that there is no practical result from a divide by
zero.
:-)
--
Stephan M. Bernsee
http://www.dspdimension.com |
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