Re: Does not have any harmonics

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Hi,

> Why does a sinusoidal waveform alone does not have any harmonics or > distortion ? > > For example, (Reference ->
> 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 > >

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.

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