Hi,
Why does a sinusoidal waveform alone does not have any harmonics or
distortion ?

For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
Sawtooth wave of constant period contains odd and even harmonics
Square wave of constant period contains odd harmonics
Triangle wave, (an integral of square wave) contains odd harmonics

But, How is it possible that sinusoidal wave alone does not have any
harmonics or distortion ?
I searched the internet,but i did not find any link/pdf that talks in
detail about these .
Any ideas ?

Thx in advans,
Karthik Balaguru

karthikbalaguru wrote:
> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?
>
> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
> Sawtooth wave of constant period contains odd and even harmonics
> Square wave of constant period contains odd harmonics
> Triangle wave, (an integral of square wave) contains odd harmonics
>
> But, How is it possible that sinusoidal wave alone does not have any
> harmonics or distortion ?
> I searched the internet,but i did not find any link/pdf that talks in
> detail about these .
> Any ideas ?
>

Just calculate the FFT of a sine wave

--
Regards, Joerg

http://www.analogconsultants.com/

A continuous sinewave with infinite duration in an ideal distortionless
transmission medium would only have the fundamental in its spectrum.
However, real-world finite duration sinewaves in distorted transmission
system would have some harmonics. These harmonics would not be as
pronounced as those of an impulse waveform. However, by running the impulse
through an integrator circuit, the harmonics can be reduced. With a series
of integrators, of course, you return to to something approaching a
sinewave. Since most radio transmission are bandwidth limited with filters,
many of the higher harmonics are hopefully missing.

"karthikbalaguru" <karthikbalaguru79@gmail.com> wrote in message
news:b7c6948d-f327-4eaa-96fc-15034bfea320@i7g2000prf.googlegroups.com...
> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?
>
> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
> Sawtooth wave of constant period contains odd and even harmonics
> Square wave of constant period contains odd harmonics
> Triangle wave, (an integral of square wave) contains odd harmonics
>
> But, How is it possible that sinusoidal wave alone does not have any
> harmonics or distortion ?
> I searched the internet,but i did not find any link/pdf that talks in
> detail about these .
> Any ideas ?
>
> Thx in advans,
> Karthik Balaguru
>
>

"karthikbalaguru" <karthikbalaguru79@gmail.com> wrote in message
news:b7c6948d-f327-4eaa-96fc-15034bfea320@i7g2000prf.googlegroups.com...
> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?
>
> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
> Sawtooth wave of constant period contains odd and even harmonics
> Square wave of constant period contains odd harmonics
> Triangle wave, (an integral of square wave) contains odd harmonics
>
> But, How is it possible that sinusoidal wave alone does not have any
> harmonics or distortion ?
> I searched the internet,but i did not find any link/pdf that talks in
> detail about these .
> Any ideas ?


As I understand it, a harmonic *is* a sine wave. So I suppose if
you consider something to contain itself, a sine wave contains a
(single) harmonic.

From http://www.ethnomusic.ucla.edu/systematic/definiti.htm :
Harmonic: Sine component of a complex signal. Thus, a complex
signal is composed of harmonics. Its frequency is obtained as
the integer multiple of the fundamental frequency

Also see:
http://www.its.bldrdoc.gov/fs-1037/dir-017/_2542.htm

-Mike

Mike is correct. A frequency spectrum consists of a positive and negative
mirror image of the waveform. This brings up all sorts of interesting
possibilities - such a SSB or single-sided sideband and DSB or double-sided
sideband.

"Mike Wahler" <mkwahler@mkwahler.net> wrote in message
news:13nl7tmti04dm35@corp.supernews.com...
>
> "karthikbalaguru" <karthikbalaguru79@gmail.com> wrote in message
> news:b7c6948d-f327-4eaa-96fc-15034bfea320@i7g2000prf.googlegroups.com...
>> Hi,
>> Why does a sinusoidal waveform alone does not have any harmonics or
>> distortion ?
>>
>> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
>> Sawtooth wave of constant period contains odd and even harmonics
>> Square wave of constant period contains odd harmonics
>> Triangle wave, (an integral of square wave) contains odd harmonics
>>
>> But, How is it possible that sinusoidal wave alone does not have any
>> harmonics or distortion ?
>> I searched the internet,but i did not find any link/pdf that talks in
>> detail about these .
>> Any ideas ?
>
>
> As I understand it, a harmonic *is* a sine wave. So I suppose if
> you consider something to contain itself, a sine wave contains a
> (single) harmonic.
>
> From http://www.ethnomusic.ucla.edu/systematic/definiti.htm :
> Harmonic: Sine component of a complex signal. Thus, a complex
> signal is composed of harmonics. Its frequency is obtained as
> the integer multiple of the fundamental frequency
>
> Also see:
> http://www.its.bldrdoc.gov/fs-1037/dir-017/_2542.htm
>
> -Mike
>
>

On 1/1/08 12:22 PM, in article 13nl89ceihsmecf@corp.supernews.com, "David
Wright" <dwright2@mc.net> wrote:

> Mike is correct. A frequency spectrum consists of a positive and negative
> mirror image of the waveform. This brings up all sorts of interesting
> possibilities - such a SSB or single-sided sideband and DSB or double-sided
> sideband.
>
> "Mike Wahler" <mkwahler@mkwahler.net> wrote in message
> news:13nl7tmti04dm35@corp.supernews.com...

(It's not nice to Top Post)

YOU are talking of modulation products, which is not what the OP was asking.

Whatever Mike had in mind, it is wrong WRT the OP's question.

>>
>> "karthikbalaguru" <karthikbalaguru79@gmail.com> wrote in message
>> news:b7c6948d-f327-4eaa-96fc-15034bfea320@i7g2000prf.googlegroups.com...
>>> Hi,
>>> Why does a sinusoidal waveform alone does not have any harmonics or
>>> distortion ?

It could have some distortion. It depends on the quality of the signal
generator. For practical purposes the distortion may not be significant,
but may be measurable.

>>>
>>> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
>>> Sawtooth wave of constant period contains odd and even harmonics
>>> Square wave of constant period contains odd harmonics
>>> Triangle wave, (an integral of square wave) contains odd harmonics.

Yes. Complex waveforms are constructed of various harmonics.

A single frequency sinewave is not a "harmonic" (it is NOT a multiple
frequency of itself)

>>>
>>> But, How is it possible that sinusoidal wave alone does not have any
>>> harmonics or distortion ?

See above.

>>> I searched the internet,but i did not find any link/pdf that talks in
>>> detail about these .
>>> Any ideas ?
>>
>>
>> As I understand it, a harmonic *is* a sine wave. So I suppose if
>> you consider something to contain itself, a sine wave contains a
>> (single) harmonic.

Nope

>>
>> From http://www.ethnomusic.ucla.edu/systematic/definiti.htm :
>> Harmonic: Sine component of a complex signal. Thus, a complex
>> signal is composed of harmonics. Its frequency is obtained as
>> the integer multiple of the fundamental frequency

OK

>>
>> Also see:
>> http://www.its.bldrdoc.gov/fs-1037/dir-017/_2542.htm
>>
>> -Mike
>>
>>
>
>

karthikbalaguru wrote:

> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?

Because it doesn't. Read up 'simple harmonic motion'.

Graham

On Tue, 01 Jan 2008 22:13:58 +0000, Eeyore
<rabbitsfriendsandrelations@hotmail.com> wrote:

>
>
>karthikbalaguru wrote:
>
>> Hi,
>> Why does a sinusoidal waveform alone does not have any harmonics or
>> distortion ?
>
>Because it doesn't. Read up 'simple harmonic motion'.

---
Q. "Daddy, why is the sky blue?"

A. "Because it is."


--
JF

On Tue, 1 Jan 2008 11:58:45 -0800 (PST), karthikbalaguru
<karthikbalaguru79@gmail.com> wrote:

>Hi,
>Why does a sinusoidal waveform alone does not have any harmonics or
>distortion ?

---
Because it's a single pure tone.
---

>For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
>Sawtooth wave of constant period contains odd and even harmonics
>Square wave of constant period contains odd harmonics
>Triangle wave, (an integral of square wave) contains odd harmonics
>
>But, How is it possible that sinusoidal wave alone does not have any
>harmonics or distortion ?

---
Every waveform which isn't a perfect sine wave is made up of more
than one sine wave, and when they combine they result in the shape
of the final waveform.
---

>I searched the internet,but i did not find any link/pdf that talks in
>detail about these .
>Any ideas ?

---
Yes. Go to this wonderful tutorial:

http://www.fourier-series.com


--
JF

On Jan 2, 12:09=A0am, John Fields <jfie...@austininstruments.com> wrote:
> On Tue, 01 Jan 2008 22:13:58 +0000, Eeyore
>
> <rabbitsfriendsandrelati...@hotmail.com> wrote:
>
> >karthikbalaguru wrote:
>
> >> Hi,
> >> Why does a sinusoidal waveform alone does not have any harmonics or
> >> distortion ?
>
> >Because it doesn't. Read up 'simple harmonic motion'.
>
> ---
> Q. "Daddy, why is the sky blue?"
>
> A. "Because it is."

You were badly brought up. My parents told me that fine dust particles
suspended in the air scattered my short wavelength light - blue light
- than longer-wavelength light - the other colours.

It didn't make much sense to me at the time - I was around four - but
at least I wasn't mis-informed.

In fact Eeyore has done a litttle better than your parents did -
"simple harmonic motion" as a search string does get you to this

http://en.wikipedia.org/wiki/Simple_harmonic_motion

which in turn points you to this

http://en.wikipedia.org/wiki/Complex_harmonic_motion

which gets you to

http://en.wikipedia.org/wiki/Harmonic_analysis

which is probably where the OP needs to go, though they may need a
fair bit of education before they can get much out of it.

--
Bill Sloman, Nijmegen

On Tue, 1 Jan 2008 11:58:45 -0800 (PST), karthikbalaguru
<karthikbalaguru79@gmail.com> wrote:

>Hi,
>Why does a sinusoidal waveform alone does not have any harmonics or
>distortion ?
>
>For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
>Sawtooth wave of constant period contains odd and even harmonics
>Square wave of constant period contains odd harmonics
>Triangle wave, (an integral of square wave) contains odd harmonics
>
>But, How is it possible that sinusoidal wave alone does not have any
>harmonics or distortion ?
>I searched the internet,but i did not find any link/pdf that talks in
>detail about these .
>Any ideas ?

Odd and even harmonics are themselves pure sine waves that are
frequency multiples of a fundamental sine wave. Distortion of a sine
wave produces odd and/or even harmonics. So, sine waves are
irreducible pure signals that other signals can be analyzed into.

--
John

"karthikbalaguru" <karthikbalaguru79@gmail.com> wrote in message
news:b7c6948d-f327-4eaa-96fc-15034bfea320@i7g2000prf.googlegroups.com...
> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?
>
> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
> Sawtooth wave of constant period contains odd and even harmonics
> Square wave of constant period contains odd harmonics
> Triangle wave, (an integral of square wave) contains odd harmonics
>
> But, How is it possible that sinusoidal wave alone does not have any
> harmonics or distortion ?
> I searched the internet,but i did not find any link/pdf that talks in
> detail about these .
> Any ideas ?
>
> Thx in advans,
> Karthik Balaguru
>
It's a good question.
Myself I'd say a triangle waveform looks like it should be the one to have
no harmonics.
But it's all down to how smoothly the waveform voltage changes. The triangle
and square have significant 'shape' discontinuities during each cycle and
these have the effect of creating harmonics.
The sine wave although a horrible looking non linear waveform, is the one
with the absolutely smoothest rate of change over all its cycle.
(DC is even smoother but isn't a frequency

John O'Flaherty wrote:

> Distortion of a sine wave produces odd and/or even harmonics.

Not QUITE correct.

Distortion as caused typically by non-linearities in a transfer
characteristic such as in an amplifier may be modelled and indeed measured
as harmonic distortion but the mechanism producing it is typically
producing a wide range of harmonic products of which typically only a few
may usually be considered of interest.

Graham,

john jardine wrote:

> Myself I'd say a triangle waveform looks like it should be the one to have
> no harmonics.

Uh ? With those rapid discontinuities ?


> But it's all down to how smoothly the waveform voltage changes.

Exactly. Simple harmonic motion. As in a child's swing or a pendulum for
example.

Graham

On Tue, 01 Jan 2008 23:52:25 +0000, Eeyore
<rabbitsfriendsandrelations@hotmail.com> wrote:

>
>
>John O'Flaherty wrote:
>
>> Distortion of a sine wave produces odd and/or even harmonics.
>
>Not QUITE correct.

Sorry, but I think it's exactly correct.

>Distortion as caused typically by non-linearities in a transfer
>characteristic such as in an amplifier may be modelled and indeed measured
>as harmonic distortion but the mechanism producing it is typically
>producing a wide range of harmonic products of which typically only a few
>may usually be considered of interest.

That's a different question.
--
John

"Fred Bartoli"

>
> It's more a matter of definition.


** No it is not - you posturing wanker.


> If you were to decompose a sine wave on a triagular waveforms base (which
> is as valid as the sine waves case),


** No it is not.

A sine wave uniquely has the property of no harmonics.

Unlike all other periodic waves, its shape is unaltered after passing
though any kind of filter.



........ Phil

Phil Allison wrote:

> "Fred Bartoli"
> >
> > It's more a matter of definition.
>
> ** No it is not - you posturing wanker.
>
> > If you were to decompose a sine wave on a triagular waveforms base (which
> > is as valid as the sine waves case),
>
> ** No it is not.
>
> A sine wave uniquely has the property of no harmonics.
>
> Unlike all other periodic waves, its shape is unaltered after passing
> though any kind of filter.

Phil's right too.

Graham

John O'Flaherty wrote:

> Eeyore wrote:
> >John O'Flaherty wrote:
> >
> >> Distortion of a sine wave produces odd and/or even harmonics.
> >
> >Not QUITE correct.
>
> Sorry, but I think it's exactly correct.

The non-linearities that are/cause distortion *result* in the production of
harmonics. They don't actually *make* harmonics.

It's a subtle distinction.

Graham

karthikbalaguru wrote:
>
> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?
>
> For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
> Sawtooth wave of constant period contains odd and even harmonics
> Square wave of constant period contains odd harmonics
> Triangle wave, (an integral of square wave) contains odd harmonics


Fourier analysis (http://en.wikipedia.org/wiki/Fourier_analysis)
demonstrates that any periodic waveform can be expressed as the sum of a
series of sine waves. The relationship between the waves frequencies of
the series is that there is one, called the fundamental, which is a sine
wave of frequency equal to that of the periodic waveform. All of the
other waves of the series have frequencies that are integer multiples of
the fundamental. These are called harmonics.

If, for your periodic wave, you select a sine wave, then the fundamental
of the series emulates it exactly. No other harmonics are needed.

> But, How is it possible that sinusoidal wave alone does not have any
> harmonics or distortion ?

Distortion is a bit different. It is a broad term that refers to a
change in a waveform between the input and output of some system.

Used in the context you, it refers to the change in harmonic content
introduced when driving a system with a pure sinusoidal input.

> I searched the internet,but i did not find any link/pdf that talks in
> detail about these .
> Any ideas ?
>
> Thx in advans,
> Karthik Balaguru

--
Paul Hovnanian mailto:Paul@Hovnanian.com
------------------------------------------------------------------
Diplomacy is the art of saying "nice doggy" while looking for a rock.

On Tue, 1 Jan 2008 15:36:10 -0800 (PST), bill.sloman@ieee.org wrote:

>On Jan 2, 12:09 am, John Fields <jfie...@austininstruments.com> wrote:
>> On Tue, 01 Jan 2008 22:13:58 +0000, Eeyore
>>
>> <rabbitsfriendsandrelati...@hotmail.com> wrote:
>>
>> >karthikbalaguru wrote:
>>
>> >> Hi,
>> >> Why does a sinusoidal waveform alone does not have any harmonics or
>> >> distortion ?
>>
>> >Because it doesn't. Read up 'simple harmonic motion'.
>>
>> ---
>> Q. "Daddy, why is the sky blue?"
>>
>> A. "Because it is."
>
>You were badly brought up.

---
Not at all.

In fact, my parents weren't technical at all, but they taught me
manners and that a library is a resource.
---

>My parents told me that fine dust particles
>suspended in the air scattered my short wavelength light - blue light
>- than longer-wavelength light - the other colours.
>
>It didn't make much sense to me at the time - I was around four - but
>at least I wasn't mis-informed.

---
Unfortunately, you were and you're obviously still in the dark about
it, not having been able to give up what you were taught even though
the truth is glaringly obvious.

Here:

http://math.ucr.edu/home/baez/physics/G ... e_sky.html
---

>In fact Eeyore has done a litttle better than your parents did -
>"simple harmonic motion" as a search string does get you to this
>
>http://en.wikipedia.org/wiki/Simple_harmonic_motion
>
>which in turn points you to this
>
>http://en.wikipedia.org/wiki/Complex_harmonic_motion
>
>which gets you to
>
>http://en.wikipedia.org/wiki/Harmonic_analysis
>
>which is probably where the OP needs to go, though they may need a
>fair bit of education before they can get much out of it.

---
LOL, you're as bad as the fucking donkey with your less than helpful
links that, by your own admission, will probably be useless.


--
JF

On Tue, 01 Jan 2008 23:52:25 +0000, Eeyore
<rabbitsfriendsandrelations@hotmail.com> wrote:

>
>
>John O'Flaherty wrote:
>
>> Distortion of a sine wave produces odd and/or even harmonics.
>
>Not QUITE correct.

---
That's _precisely_ correct.

For instance, what happens when you run a perfect sine wave through
a diode?
---

>Distortion as caused typically by non-linearities in a transfer
>characteristic such as in an amplifier may be modelled and indeed measured
>as harmonic distortion but the mechanism producing it is typically
>producing a wide range of harmonic products of which typically only a few
>may usually be considered of interest.

---
So what?

It's the nonlinearity of the transfer function which is causing the
distortion and, ergo, the generation of the harmonic products.


--
JF

On Jan 2, 3:58=A0am, karthikbalaguru <karthikbalagur...@gmail.com>
wrote:
> Hi,
> Why does a sinusoidal waveform alone does not have any harmonics or
> distortion ?
>
> For example, (Reference ->http://en.wikipedia.org/wiki/Waveform),
> Sawtooth wave of constant period contains odd and even harmonics
> Square wave of constant period =A0contains odd harmonics
> Triangle wave, (an integral of square wave) contains odd harmonics
>
> But, How is it possible that sinusoidal wave alone does not have any
> harmonics or distortion ?
> I searched the internet,but i did not find any link/pdf that talks in
> detail about these .
> Any ideas ?

> Thx in advans,
> Karthik Balaguru
Hi,
You may need to read or on some basic harmonic theory.

Waveforms that are symmetrical above and below their HORIZONTAL
CENTERLINES (does not necessaryly have to be at x-axis) contain no
even-numbered harmonics. Sawtooth wave is not symmetrical above and
below their horizontal centerlines hence you have both odd and even
harmonics.Whereas square and triangle wave is symmetrical above and
below their horizontal centerlines hence you only have odd-numbered
harmonics.
ref: http://www.allaboutcircuits.com/vol_2/chpt_7/4.html
--
M Zhafran

On Wed, 2 Jan 2008 11:06:56 +1100, "Phil Allison"
<philallison@tpg.com.au> wrote:

>
>"Fred Bartoli"
>
>>
>> It's more a matter of definition.
>
>
>** No it is not - you posturing wanker.
>
>
>> If you were to decompose a sine wave on a triagular waveforms base (which
>> is as valid as the sine waves case),
>
>
>** No it is not.
>
> A sine wave uniquely has the property of no harmonics.
>
> Unlike all other periodic waves, its shape is unaltered after passing
>though any kind of filter.
>
>
>
>....... Phil

---
Nice...


--
JF

On Wed, 02 Jan 2008 00:14:47 +0000, Eeyore
<rabbitsfriendsandrelations@hotmail.com> wrote:

>
>
>John O'Flaherty wrote:
>
>> Eeyore wrote:
>> >John O'Flaherty wrote:
>> >
>> >> Distortion of a sine wave produces odd and/or even harmonics.
>> >
>> >Not QUITE correct.
>>
>> Sorry, but I think it's exactly correct.
>
>The non-linearities that are/cause distortion *result* in the production of
>harmonics. They don't actually *make* harmonics.
>
>It's a subtle distinction.

---
Bullshit.

O'Flaherty wrote:

"Distortion of a sine wave produces odd and/or even harmonics."

which, no matter how fine you slice it, is true.


--
JF

bill.sloman@ieee.org wrote:
>
> You were badly brought up. My parents told me that fine dust particles
> suspended in the air scattered my short wavelength light - blue light
> - than longer-wavelength light - the other colours.


I'll bet they told you that you were worth something, too.


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida