# Does not have any harmonics

• posted

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

• posted

Just calculate the FFT of a sine wave :-)

```--
Regards, Joerg

http://www.analogconsultants.com/```
• posted

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

• posted

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.

```--
Regards,

John Popelish```
• posted

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```
• posted

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

• posted

It is really quite simple, can you integrate it or differentiate it once or more times and have a self similar repetitive signal?

There are very few waveshapes that can to that.

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