Does not have any harmonics

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:

-- M Zhafran

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Nice...

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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.

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

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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

Picture a rotating disk on a horizontal axis, with a dot near its edge, and you are looking at that dot from the axis. The disk is spinning at a fixed speed (constant rotations per minute, perhaps), so its rotational cycle represents a perfect single frequency.

The vertical height of the dot (with zero height being the height of the axis) produces a perfect sine wave as time passes, if you call time zero a moment when the dot was beside the axis. The horizontal position of the dot, with zero position being he axis, is a perfect cosine wave. So either the sine wave or the cosine wave is a representation of the single rotational frequency of the disk. The combination of the sine and cosine components of the dot's position completely describe its rotational cycle at one pure frequency.

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Regards,

John Popelish

... as long as the filter consists only of passive/linear components :-).

Reading all the responses to this has been like hearing of all the wise, blind men who are describing an elephant.

So, IMHO, an elephant is like a rope. And by the way, why is it suddenly raining fertilizer?

At any rate, a sine wave doesn't have any because that's how harmonics are defined. Harmonics are defined in the context of the Fourier series, and the Fourier series for a pure sine wave is just -- that sine wave. That's it, no more. Only a periodic wave that deviates from a perfect sine wave can have harmonics, and (thanks to Fourier) we know that we can express that periodic wave, if we so choose, as a sum of sine waves at the fundamental frequency and all of it's multiples.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
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Most people have no clue what they are talking about.

Sinusodial's don't have "harmonics" because that is what we are using to decompose the signal into. If it did then it wouldn't make any sense.

Basically we have some process, call it P, that when it acts on something returns a decomposition into "special" objects say, S1, ..., Sn that depends on that object.

Something like P(x) = S1(x) + ... + Sn(x)

But we expect that we we decompose one of the special objects we should get it back... else it wouldn't be so special and mathematically wouldn't make any sense.

Just so happens that sin waves have very nice properties but guess what? The do have harmonics!!!?!?!?!! if you take your "special" objects as something else(such as wavelets).

Basically there is a theorem in mathematics that says you can write any function(well, there are some conditions) as a sum of sinusoids. This is the decomposition. But its obvious that the only way to write a sinusoid in terms of a sinusoid is the sinusoid itself. i.e., sin(x) === sin(x)... but x^2 === sum(sinusoids).

All that stuff is whats called fourier analysis but in fact is much more general. Wavelets do a similar thing by decomposing functions(signals) using a different basis and a slightly different principle. In those systems one might say that sinusoids do have harmonics because sinusoids are not "simple".

If you are familiar with polynomials then its similar.

You might say that every function that is expressiable as a polynomial(taylor series, for example), has polynomial harmonics... but the simple function x, x^2, x^3, etc... have no harmonics. Why? Because they are simple in that system. They are not simple in when the basis is sinusoids.(just as sinusoids are not simple when the basis is polynomials)

In short, your answer is that it does have sinusoidal harmonics... they are all just zero.

That the elementary chemicals in the human body were worth about six pence. It was a joke.

-- Bill Sloman, Nijmegen

of

For people who aren't in the habit of choosing their words carefully.

-- Bill Sloman, Nijmegen

On Jan 1, 3:46 pm, John O'Flaherty wrote: [....]

Place "time independent" in front of "distortion" for a more accurate answer. An extreme example of the case is:

1N400X IN--->!----+------Scope ! ) ) 680uH ) ! GND

Tune the signal generator for resonance between the diode and the inductor and adjusts tha amplitude around 1V and observe.

So, sine waves are

As is the help you gave the OP.

In short, because air is blue.

But that's *HOW* the sky is blue.

Nobody knows *WHY*, other than "because that's the way it is."

Cheers! Rich

simple answer.. saw and square waves are made up of hundreds of sine waves.. sine wave is made up of one.

NO.

Surely you know of Rayleigh scattering.

It doesn't require DUST in the air for the skyy to look blue. The very air molecules themselves are sufficient.

ALSO: Wiki "water", and you'll find that pure H2O is blue-green in colour, i.e. in its absorption spectrum. That blue-green colour arises from TWO mechanisms:

1) Optical absorption from bend/stretch/whatever in Willy Water Molecule (who is bent!)

2) Rayleigh scattering from the molecules themselves.

Interestingly, D2O (heavy water) only exhibits effect (2) within the visible part of the EM spectrum so should look LESS blue than H2O. That is because the higher mass of the D atoms shifts the frequencies into the IR region.

H2O absorbs ONE HUNDRED TIMES more at the far red end of visible than at the far blue end. Quite interesting!

Not true at all; see above and Wikipedia.

Martin

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M.A.Poyser                                                  Tel.: 07967 110890
Manchester, U.K.          http://www.livejournal.com/userinfo.bml?user=fleetie

Hundreds?

On Wed, 02 Jan 2008 21:04:20 +0000, Fleetie wrote: I wrote, but flemmy snipped the attribution:

Yes. As I've said, that's _how_ the sky is blue, i.e., the mechanism. ("Rayleigh Scattering" is just another $.50 word for "air is blue". ;-)

But that does nothing to address _why_ it's that way.

Cheers! Rich

No, it's infinity, but above some number of them their amplitudes go below any measurable value.

Cheers! Rich

You *are* posting as Rich the Crap Philosopher here?

In this particular case, the explanation of how the sky is blue is a perfectly adequate explanation of why the sky is blue.

A sufficiently daft theologian might explain that God fudged the laws of physics to make the sky blue because she liked the colour blue, but that would just be moving the goal-posts.

-- Bill Sloman, Nijmegen