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my question maybe seems very simple but, I'm not familiar with the answer of that;

what is the meaning of harmonic of the signal exactly?

I know the harmonics of the signal are signals whoes frequencies are multiple of the frequency of the fundamental component of the main signal but I want to know about the deep concept of that, actually; my exact question is:

what is the meaning of having harmonic?

or

some signal has harmonic and some other not; what is the difference between these two signal in properties?

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    \$\begingroup\$ The answer largely depends on context. For example, when dealing with power quality, "harmonics" are generally considered a "bad" factor and the concept of total harmonic distortion (THD) comes into play, because most signals are desired to be single ("clean") sines. However there are signals in which THD is irrelevant, like the clock signal in a digital circuit. What you should keep in mind: the closer a signal is to a sine wave, the less harmonic content. \$\endgroup\$ – Vicente Cunha May 24 '18 at 6:28
  • \$\begingroup\$ @Vicente Cunha thanks very much. I also have other question; when a special signal not clean, what is the property of that, I mean the harmonics are caused by what? \$\endgroup\$ – hojjat May 24 '18 at 7:05
  • \$\begingroup\$ Again, context is key, but the generic answer is non-linearities. In power quality, non-linear loads and switching electronics are usually the cause. A linear system will never "create" harmonic content. To improve the overall quality of this question, you should provide some sort of context or example to it, so that answers can be meaningful. \$\endgroup\$ – Vicente Cunha May 24 '18 at 7:21
  • \$\begingroup\$ @ Vicente Cunha bless you Mr. your comments were useful \$\endgroup\$ – hojjat May 24 '18 at 7:29
  • \$\begingroup\$ @hojjat: Vincente has suggested that you improve your question with context. Will you? \$\endgroup\$ – Transistor May 24 '18 at 8:42
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what is the meaning of having harmonic?

  • A signal with no harmonics is fundamentally a sine wave

A sine wave has spectral content only at one exact frequency

  • A signal WITH harmonics IS NOT a sine wave

A sine wave can be made to have harmonic content by passing it through a non-linear amplifier: -

enter image description here

The perfect input sine wave is transformed into a new waveform due to the non-linear shape of the amplifier's characteristic. The reverse can also happen; a triangle wave can nearly be converted back to a sine wave i.e. its harmonic content can be significantly reduced by a non-linear amplifier: -

enter image description here

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Perform an Internet search using these keywords:

fourier transform harmonics

For a specific example, try a search using these keywords:

square wave fourier transform harmonics

You can find some useful videos on YouTube that demonstrate the concepts of Fourier transforms, fundamentals, harmonics, etc. For example:

Fourier Series Animation (Square Wave)

(^^- This is a visual example that adds odd harmonics (n=1,3,5,7) to build a square wave signal.)

Sine Wave to Square Wave Using Fourier Series

(^^- This is an auditory example. It's a bit loud, so be forewarned!)

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  • \$\begingroup\$ Interesting videos, I still have not learned about harmonics or Fourier, While i understand that a square wave can be represented as the sum of those other waves does that mean they are actually there? \$\endgroup\$ – Edwin Fairchild May 24 '18 at 6:22
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    \$\begingroup\$ @EdwinFairchild It should be understood that Fourier and harmonic decomposition are just mathematical tools. It is an integral transform that is helpful for solving differential equations and understanding dynamics of systems. Think about what "actually there" really means. A philosophically similar question would be: I know 2 = 1+1, but are the ones actually there? \$\endgroup\$ – Vicente Cunha May 24 '18 at 6:35
  • \$\begingroup\$ @Edwin Fairchild you can also follow this amazing video(with complete explanation)on youtube that models square wave youtu.be/SpzNQOOBeRg \$\endgroup\$ – hojjat May 24 '18 at 7:10
  • \$\begingroup\$ @hojjat oh that was good too!! what is the reason behind using odd numbers? \$\endgroup\$ – Edwin Fairchild May 24 '18 at 8:06
  • \$\begingroup\$ I wonder if there is any software where i can play with these sort of things.. or maybe I can design this in hardware? Something like two different Wien bridge oscillators, but how would i know what frequency a 3rd harmonic is at? I guess i've got quite a bit to learn \$\endgroup\$ – Edwin Fairchild May 24 '18 at 8:07
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Harmonics do not exist. A flip-flip, dividing by two, does not intentionally produce harmonics; instead the flip-flop produces a perfect 50% duty-cycle squarewave, with very fast edge transitions (1 nanosecond, for example).

The math we use consists of many correlations. The Fourier Transform is just a way to implement correlations, with a precise integer-related time base for each correlation.

This precise integer-related time-base causes the math to provide very sharp output values for integer-related correlation-time-bases.

We call these sharp output values the "Harmonics".

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  • \$\begingroup\$ "Harmonics do not exist" - uh. What? Yes they do. I think you understand this correctly but you're not explaining it very well. Harmonics are actually mandatory for some kinds of signals to exist in their desired form. \$\endgroup\$ – Reinderien May 26 '18 at 16:44
  • \$\begingroup\$ @analogsystemsrf what's your intention of writing "harmonics do not exist" exactly? \$\endgroup\$ – hojjat May 26 '18 at 17:44

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