Does not have any harmonics

Just calculate the FFT of a sine wave :-)

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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.

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

: 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:

-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.

(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.

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.

Yes. Complex waveforms are constructed of various harmonics.

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

See above.

Nope

OK

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

Graham

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

A. "Because it is."

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

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

which in turn points you to this

which gets you to

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

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

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 :)

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,

Uh ? With those rapid discontinuities ?

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

Graham

john jardine a écrit :

It's more a matter of definition. When you take the view of decomposing a waveform on a sine waves base, it is not abnormal that a sine wave has just one component on that base: itself. The contrary would be abnormal.

If you were to decompose a sine wave on a triagular waveforms base (which is as valid as the sine waves case), it'd had lots of 'harmonics' and a triangular waveform would have just the fundamental.

--
Thanks,
Fred.

Sorry, but I think it's exactly correct.

That's a different question.

--
John

"Fred Bartoli"

** No it is not - you posturing wanker.

** 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's right too.

Graham

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

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.

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.

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