| Author |
Message |
Michael
Guest
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 Posted:
Sun Dec 12, 2004 3:35 am Post subject:
Struggling with waveform questions. |
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Hi,
I'm having to work through a bunch of waveform questions and a few
have them really have me stumped. I'd appreciate if anybody can give
me the help I need to answer the following questions:
1. State what parameters of the harmonic content need to have a
precise values in order to generate a particular periodic waveform.
2. State what can limit the accuracy of a fourier series approximation
to a periodic unsampled waveform.
3. State what can affect the shape of a waveform after sampling and
then smoothing to a continous waveform.
I'd really appreciate any pointers.
Thanks guys. |
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Randy Yates
Guest
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| Posted:
Sun Dec 12, 2004 3:42 am Post subject:
Re: Struggling with waveform questions. |
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mikelar10@yahoo.co.uk (Michael) writes:
| Quote: | Hi,
I'm having to work through a bunch of waveform questions and a few
have them really have me stumped. I'd appreciate if anybody can give
me the help I need to answer the following questions:
1. State what parameters of the harmonic content need to have a
precise values in order to generate a particular periodic waveform.
|
Ya' got me.
| Quote: | 2. State what can limit the accuracy of a fourier series approximation
to a periodic unsampled waveform.
|
Look up/reread the Dirichlet conditions.
| Quote: | 3. State what can affect the shape of a waveform after sampling and
then smoothing to a continous waveform.
|
What's the first thing one does when converting an analog signal to
digital?
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124 |
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Randy Yates
Guest
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| Posted:
Sun Dec 12, 2004 3:45 am Post subject:
Re: Struggling with waveform questions. |
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Randy Yates <randy.yates@sonyericsson.com> writes:
| Quote: | mikelar10@yahoo.co.uk (Michael) writes:
Hi,
I'm having to work through a bunch of waveform questions and a few
have them really have me stumped. I'd appreciate if anybody can give
me the help I need to answer the following questions:
1. State what parameters of the harmonic content need to have a
precise values in order to generate a particular periodic waveform.
Ya' got me.
|
I think I get what they're after here now: Is the Fourier series simply
the magnitude of the harmonics? (Hint: No.)
--
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
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| Posted:
Sun Dec 12, 2004 4:01 am Post subject:
Re: Struggling with waveform questions. |
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Michael wrote:
| Quote: | Hi,
I'm having to work through a bunch of waveform questions and a few
have them really have me stumped. I'd appreciate if anybody can give
me the help I need to answer the following questions:
1. State what parameters of the harmonic content need to have a
precise values in order to generate a particular periodic waveform.
|
I think that question is poorly worded. Maybe putting it differently
will help. How are the components necessarily related in a periodic
waveform that has more than one frequency?
| Quote: | 2. State what can limit the accuracy of a fourier series approximation
to a periodic unsampled waveform.
3. State what can affect the shape of a waveform after sampling and
then smoothing to a continous waveform.
|
That's another poorly worded question. I don't know what it's intended
to mean, but it it might mean lots i=of things. Try this: You sample a
waveform (presumably respecting the bandwith requirements) and then
reconstruct it. So now you have this continuous signal and the question
is, what can affect its shape? How about an analog filter, or a
rectifier, or ...? Dollars to donuts, that's not the answer the prof
wants, but it's a valid answer to the question he asked. You can't very
well tell him to learn to express himself in English or find another
profession, but you might be able to show him this reply.
| Quote: | I'd really appreciate any pointers.
Thanks guys.
|
You have my sympathy.
Jerry
--
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:
Sun Dec 12, 2004 7:54 am Post subject:
Re: Struggling with waveform questions. |
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Michael wrote:
| Quote: |
Hi,
I'm having to work through a bunch of waveform questions and a few
have them really have me stumped. I'd appreciate if anybody can give
me the help I need to answer the following questions:
|
I hope this isn't homework :-).
| Quote: | 1. State what parameters of the harmonic content need to have a
precise values in order to generate a particular periodic waveform.
|
For each harmonic you need to specify its amplitude and its phase relationship
to the zeroth harmonic.
| Quote: | 2. State what can limit the accuracy of a fourier series approximation
to a periodic unsampled waveform.
|
Assuming that both time and amplitude are continuous (ie not discrete),
then for a truely periodic waveform the fourier series is an exact
representation. However, the Fourier series is usually an infinite sum
and if this infinite sum is truncated, then the truncated Fourier series
is only an approximation.
| Quote: | 3. State what can affect the shape of a waveform after sampling and
then smoothing to a continous waveform.
|
Sampling should limit the bandwidth of the waveform before the sampling
takes place. Limiting the bandwith with a low pass filter can change the
shap of the waveform.
I don't know what you mean by smoothing in this context.
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam@mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
"Open source is an intellectual-property destroyer. I can't
imagine something that could be worse than this for the software
business and the intellectual-property business."
-- Jim Allchin, Microsoft |
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Fred Marshall
Guest
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| Posted:
Mon Dec 13, 2004 4:52 am Post subject:
Re: Struggling with waveform questions. |
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Erik,
a nit below:
Fred
"Erik de Castro Lopo" <nospam@mega-nerd.com> wrote in message
news:41BBB2DD.749CF480@mega-nerd.com...
| Quote: | Michael wrote:
Hi,
I'm having to work through a bunch of waveform questions and a few
have them really have me stumped. I'd appreciate if anybody can give
me the help I need to answer the following questions:
I hope this isn't homework :-).
1. State what parameters of the harmonic content need to have a
precise values in order to generate a particular periodic waveform.
For each harmonic you need to specify its amplitude and its phase
relationship
to the zeroth harmonic.
|
***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. |
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Peter K.
Guest
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| Posted:
Mon Dec 13, 2004 6:59 am Post subject:
Re: Struggling with waveform questions. |
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Fred wrote:
] ***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.
Are you saying that the fundamental (= zeroth (sp?) harmonic) doesn't
have phase?
That doesn't sound right to me... but it's too late at night for
coherent thought.
Ciao,
Peter K. |
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Jerry Avins
Guest
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| Posted:
Mon Dec 13, 2004 6:59 am Post subject:
Re: Struggling with waveform questions. |
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Peter K. wrote:
| Quote: | Fred wrote:
] ***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.
Are you saying that the fundamental (= zeroth (sp?) harmonic) doesn't
have phase?
That doesn't sound right to me... but it's too late at night for
coherent thought.
Ciao,
Peter K.
|
If the second harmonic is an octave higher than the fundamental, doesn't
that define the fundamental as the first harmonic and DC as the zeroth?
DC has no phase. I'm with Fred. :-)
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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Stephan M. Bernsee
Guest
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| Posted:
Mon Dec 13, 2004 6:59 am Post subject:
Re: Struggling with waveform questions. |
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On 2004-12-13 00:52:51 +0100, "Fred Marshall"
<fmarshallx@remove_the_x.acm.org> said:
| Quote: | ***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...
--
Stephan M. Bernsee
http://www.dspdimension.com |
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Peter J. Kootsookos
Guest
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| Posted:
Mon Dec 13, 2004 5:11 pm Post subject:
Re: Struggling with waveform questions. |
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"Jerry Avins" <jya@ieee.org> wrote
| Quote: | If the second harmonic is an octave higher than the fundamental, doesn't
that define the fundamental as the first harmonic and DC as the zeroth?
DC has no phase. I'm with Fred. :-)
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:-) D'oh. |
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Rick Lyons
Guest
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| Posted:
Mon Dec 13, 2004 7:29 pm Post subject:
Re: Struggling with waveform questions. |
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On Sun, 12 Dec 2004 22:50:50 -0500, Jerry Avins <jya@ieee.org> wrote:
| Quote: | Peter K. wrote:
Fred wrote:
] ***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.
Are you saying that the fundamental (= zeroth (sp?) harmonic) doesn't
have phase?
That doesn't sound right to me... but it's too late at night for
coherent thought.
Ciao,
Peter K.
If the second harmonic is an octave higher than the fundamental, doesn't
that define the fundamental as the first harmonic and DC as the zeroth?
DC has no phase. I'm with Fred. :-)
Jerry
|
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?
Am I mistaken here?
This is the problem that happens when someone creates
new strange & undefined terminology like "zeroeth harmonic".
Nobody knows, for sure, what the heck it means.
[-Rick-] |
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Stephan M. Bernsee
Guest
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| Posted:
Mon Dec 13, 2004 7:42 pm Post subject:
Re: Struggling with waveform questions. |
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On 2004-12-13 15:29:36 +0100, r.lyons@_BOGUS_ieee.org (Rick Lyons) said:
| Quote: | 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).
--
Stephan M. Bernsee
http://www.dspdimension.com |
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Randy Yates
Guest
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| Posted:
Mon Dec 13, 2004 7:50 pm Post subject:
Re: Struggling with waveform questions. |
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Stephan M. Bernsee <spam@dspdimension.com> writes:
| Quote: | 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."
--
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:
Mon Dec 13, 2004 8:06 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...
|
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. |
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Jerry Avins
Guest
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| Posted:
Mon Dec 13, 2004 8:25 pm Post subject:
Re: Struggling with waveform questions. |
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Rick Lyons wrote:
| Quote: | On Sun, 12 Dec 2004 22:50:50 -0500, Jerry Avins <jya@ieee.org> wrote:
Peter K. wrote:
Fred wrote:
] ***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.
Are you saying that the fundamental (= zeroth (sp?) harmonic) doesn't
have phase?
That doesn't sound right to me... but it's too late at night for
coherent thought.
Ciao,
Peter K.
If the second harmonic is an octave higher than the fundamental, doesn't
that define the fundamental as the first harmonic and DC as the zeroth?
DC has no phase. I'm with Fred. :-)
Jerry
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?
Am I mistaken here?
This is the problem that happens when someone creates
new strange & undefined terminology like "zeroeth harmonic".
Nobody knows, for sure, what the heck it means.
|
You are indeed, to my astonishment, mistaken.
Consider the push-pull amplifier. It's symmetry eliminates
second-harmonic distortion; in fact, all even-harmonic distortion.
Consider a symmetrical square wave. It consists entirely of odd
harmonics, numbers 1, 3, 5, etc. If the basic frequency -- i.e., the
fundamental, is 1 Hz, the second harmonic would be 2 Hz. if a little
imbalance allowed it to appear.
It'd just a definition: first harmonic == fundamental. Linguistically,
that's ugly. As a definition, it simplifies the math.
However strange one thinks the notion of "zeroeth harmonic" as DC, it is
justified because we number all other harmonics by their place in the
Fourier series that describes the waveform. Why not that one too?
Jerry
--
Engineering is the art of making what you want from things you can get.
ŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻŻ |
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