| Author |
Message |
Jerry Avins
Guest
|
 Posted:
Mon Dec 13, 2004 8:35 pm 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...
|
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
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Stan Pawlukiewicz
Guest
|
| Posted:
Mon Dec 13, 2004 8:40 pm Post subject:
Re: Struggling with waveform questions. |
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Jerry Avins wrote:
| 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...
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
|
I don't like the notion of DC being a harmonic. It would be a harmonic
of all signals. |
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Jerry Avins
Guest
|
| Posted:
Mon Dec 13, 2004 8:49 pm Post subject:
Re: Struggling with waveform questions. |
|
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Randy Yates wrote:
| Quote: | Stephan M. Bernsee <spam@dspdimension.com> writes:
On 2004-12-13 15:29:36 +0100, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:
Hi,
As far as I knew the second harmonic is not an octave higher. If
the "fundamental" is 1 kHz, isn't the first harmonic 1 + 1 = 2 kHz?
And is not the second harmonic 1 + 1 + 1 = 3 kHz?
Nope. Actually, the first harmonic *is* [quite often but not always]
the fundamental. You're probably thinking of the first *overtone*,
which is a term sometimes used interchangeably - and incorrectly.
So, the second harmonic is one octave higher and the third is one
fifth (musical interval) higher than the second. The zeroth harmonic
doesn't really make sense - it would be at DC (0 Hz).
Being in the business, I have no doubt that you're correct in terms
of usage, Stephan, but "in my book" the fundamental is not a harmonic.
I would say that the terminology is semantically incorrect but has come
to be used in this manner in the field. This is supported by the definitions
given by www.webster.com for "harmonic" (the noun form) and "overtone."
|
Linguistically, the fundamental is not a harmonic. Technically, it is
the first element of the series of harmonics, and therefore called the
first (member of the) harmonic (series).* Whether or not you accept
that, the second harmonic is an octave higher than the fundamental. I
will cite texts to support that statement if you like.
Jerry
________________________________________
* I don't mean 1, 1/2, 1/3, 1/4, ...
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Randy Yates
Guest
|
| Posted:
Mon Dec 13, 2004 9:00 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Jerry Avins <jya@ieee.org> writes:
| Quote: | Randy Yates wrote:
Stephan M. Bernsee <spam@dspdimension.com> writes:
On 2004-12-13 15:29:36 +0100, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:
Hi,
As far as I knew the second harmonic is not an octave higher. If
the "fundamental" is 1 kHz, isn't the first harmonic 1 + 1 = 2 kHz?
And is not the second harmonic 1 + 1 + 1 = 3 kHz?
Nope. Actually, the first harmonic *is* [quite often but not always]
the fundamental. You're probably thinking of the first *overtone*,
which is a term sometimes used interchangeably - and incorrectly.
So, the second harmonic is one octave higher and the third is one
fifth (musical interval) higher than the second. The zeroth harmonic
doesn't really make sense - it would be at DC (0 Hz).
Being in the business, I have no doubt that you're correct in terms
of usage, Stephan, but "in my book" the fundamental is not a harmonic.
I would say that the terminology is semantically incorrect but has come
to be used in this manner in the field. This is supported by the definitions
given by www.webster.com for "harmonic" (the noun form) and "overtone."
Linguistically, the fundamental is not a harmonic. Technically, it is
the first element of the series of harmonics, and therefore called the
first (member of the) harmonic (series).*
|
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.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124 |
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Jerry Avins
Guest
|
| Posted:
Mon Dec 13, 2004 9:19 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Stan Pawlukiewicz wrote:
| Quote: | ... 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?
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. 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."
According to that, if the fundamental frequency is F, the frequencies
defined by the integers 0, 1, and 2 are DC, F, and 2F.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
|
| Posted:
Mon Dec 13, 2004 9:21 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Stan Pawlukiewicz wrote:
...
| Quote: | 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.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
|
| Posted:
Mon Dec 13, 2004 10:15 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Randy Yates wrote:
...
| Quote: | 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",
a point not everyone understands. Similarly, it follows from the
definition of "nth harmonic" that "zeroth harmonic" denotes DC. I agree
that it's ugly.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Randy Yates
Guest
|
| Posted:
Mon Dec 13, 2004 10:32 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Jerry Avins <jya@ieee.org> writes:
| Quote: | 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?
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124 |
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Eric Jacobsen
Guest
|
| Posted:
Mon Dec 13, 2004 10:49 pm Post subject:
Re: Struggling with waveform questions. |
|
|
On Mon, 13 Dec 2004 10:35:20 -0500, Jerry Avins <jya@ieee.org> wrote:
| 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...
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
|
There's an exception, but I'll bet that a lot of people don't like the
idea much. I expect that this has the potential for a lot of
philosophical discussion, but, anyway...
A complex signal at baseband (yeah, here we go) can have a component
at DC. Because it has two orthogonal components (aka I and Q), it can
have a phase.
Many OFDM systems leave the center tone or tones unused because
putting modulation there disturbs DC-offset control loops or gets
corrupted by LO bleed-through in direct conversion systems. Without
those problems, though, a theoretical system can easily have
information modulated at DC with both magnitude and phase.
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org |
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Eric Jacobsen
Guest
|
| Posted:
Mon Dec 13, 2004 10:54 pm Post subject:
Re: Struggling with waveform questions. |
|
|
On Mon, 13 Dec 2004 10:49:53 -0500, Jerry Avins <jya@ieee.org> wrote:
| Quote: | Randy Yates wrote:
Stephan M. Bernsee <spam@dspdimension.com> writes:
On 2004-12-13 15:29:36 +0100, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:
Hi,
As far as I knew the second harmonic is not an octave higher. If
the "fundamental" is 1 kHz, isn't the first harmonic 1 + 1 = 2 kHz?
And is not the second harmonic 1 + 1 + 1 = 3 kHz?
Nope. Actually, the first harmonic *is* [quite often but not always]
the fundamental. You're probably thinking of the first *overtone*,
which is a term sometimes used interchangeably - and incorrectly.
So, the second harmonic is one octave higher and the third is one
fifth (musical interval) higher than the second. The zeroth harmonic
doesn't really make sense - it would be at DC (0 Hz).
Being in the business, I have no doubt that you're correct in terms
of usage, Stephan, but "in my book" the fundamental is not a harmonic.
I would say that the terminology is semantically incorrect but has come
to be used in this manner in the field. This is supported by the definitions
given by www.webster.com for "harmonic" (the noun form) and "overtone."
Linguistically, the fundamental is not a harmonic. Technically, it is
the first element of the series of harmonics, and therefore called the
first (member of the) harmonic (series).* Whether or not you accept
that, the second harmonic is an octave higher than the fundamental. I
will cite texts to support that statement if you like.
Jerry
________________________________________
* I don't mean 1, 1/2, 1/3, 1/4, ...
|
Thanks, Jerry! Finally an explanation that fits my intuition enough
that it has a hope of sticking in my brain.
I've posted before (many moons ago) that this terminology always
seemed weird to me, and it seemed to me that this was a good case
where the zero-based indexing made more sense so that what we're
calling the first harmonic here should be the zeroth, and the second
the first. My intuition was that it had to have something with which
to be in harmony, so it was the "first" harmonic. This resulted in a
lot of confusion, of course, because only me and other similarly
confused people used the term that way, and all the right-thinking
folks just thought we were inept or incompetent. ;)
Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org |
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Jerry Avins
Guest
|
| Posted:
Mon Dec 13, 2004 11:20 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Randy Yates wrote:
| Quote: | 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. Look for any definition in a physics text. Many
words in technical use have meanings that differ from their common ones.
Force. Harmonic. Power. Impulse. Resistance. Work. Fatigue. ...
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Jerry Avins
Guest
|
| Posted:
Mon Dec 13, 2004 11:29 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Eric Jacobsen wrote:
...
| Quote: | ... a theoretical system can easily have
information modulated at DC with both magnitude and phase.
|
???? Modulation implies change of some sort. How can unchanging voltage
carry modulation? How much time does a one-degree phase shift at DC imply?
If the notion of a complex baseband signal -- we already agreed that it
can't exist on a single wire -- implies that we can assign arbitrary DC
phases, there are holes in the theory that need patching.
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Randy Yates
Guest
|
| Posted:
Mon Dec 13, 2004 11:34 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Jerry Avins <jya@ieee.org> writes:
| Quote: | 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.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124 |
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Jon Harris
Guest
|
| Posted:
Mon Dec 13, 2004 11:44 pm Post subject:
Re: Struggling with waveform questions. |
|
|
"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpwtvm5k1h.fsf@usrts005.corpusers.net...
| Quote: | Stephan M. Bernsee <spam@dspdimension.com> writes:
On 2004-12-13 15:29:36 +0100, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:
Hi,
As far as I knew the second harmonic is not an octave higher. If
the "fundamental" is 1 kHz, isn't the first harmonic 1 + 1 = 2 kHz?
And is not the second harmonic 1 + 1 + 1 = 3 kHz?
Nope. Actually, the first harmonic *is* [quite often but not always]
the fundamental. You're probably thinking of the first *overtone*,
which is a term sometimes used interchangeably - and incorrectly.
So, the second harmonic is one octave higher and the third is one
fifth (musical interval) higher than the second. The zeroth harmonic
doesn't really make sense - it would be at DC (0 Hz).
Being in the business, I have no doubt that you're correct in terms
of usage, Stephan, but "in my book" the fundamental is not a harmonic.
I would say that the terminology is semantically incorrect but has come
to be used in this manner in the field. This is supported by the definitions
given by www.webster.com for "harmonic" (the noun form) and "overtone."
|
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 haven't checked scientific or engineering dictionaries to see what they say,
but two music dictionaries I looked at made the same distinction between
harmonics and overtones:
http://www.dolmetsch.com/defso.htm
http://musicnet.chandra.ac.th/eng/mus_dic.htm#GlossaryO
So despite what Webster says, the 2 terms are not strictly synonymous according
to music dictionaries and probably common definitions in engineering. |
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Richard Dobson
Guest
|
| Posted:
Mon Dec 13, 2004 11:44 pm Post subject:
Re: Struggling with waveform questions. |
|
|
Let me give the canonical musical position on all this, drawing solely on
physical models. The canonical model for the vibrations of a musical note is
that of the stretched string fixed at both ends (the monochord). When excited,
this exhibits one or more "modes of vibration", which in the case of the "ideal
string" are in harmonic relationship and are thus casually referred to as
harmonics. The longest mode of vibration corresponds to the length of the string
and is thus the "fundamental", or "first harmonic". The modes of vibration zre
found from successive integral divisions of the string (naturally we do not
consider a division by zero here!).
In the case of the fundamental, there is ~one~ antinode in the middle (maximum
excursion): the ends of the string are in effect nodes. In the case of the
second harmonic (one octave), there is a node in the centre, and ~two~ antinodes
at the bisection of each half wavelength. Thus one can count harmonics by
counting the number of antinodes.
In the case of a modern piano, the stiffness of the strings relative to their
diameter is such that higher harmonics are "stretched" with respect to the
fundamental; e.g. the 2nd harmonic is a tad sharper than a true octave.
In the domain of music and acoustics, therefore, the first harmonic = the
fundamental; the frequency of the Nth harmonic (in the absence of other factors)
is N * Fundamental_Frequency.
In the end, it is a conflict betwwen the use of cardinal v ordinal numbers.
Musicians have them correspond as I have shown. I firmly believe this to be
fully correct, and also appropriate for engineers and mathematicians to use, as
for musicians.
Reference: Fundamentals of Music Acoustics, Arthur H Benade 1975
Richard Dobson
Randy Yates wrote:
| Quote: | 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? |
|
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