Why Does a Square Wave Contain Only Odd Harmonics?

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Discussion Overview

The discussion centers on the characteristics of square waves, specifically why they contain only odd harmonics of the fundamental frequency. Participants explore the implications of this phenomenon, including the role of even harmonics and the potential influence of the square wave's duty cycle.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that square waves are odd functions, which leads to the cancellation of even harmonics.
  • One participant notes that the Fourier expansion of a square wave includes only odd harmonics, suggesting that even harmonics are inherently absent.
  • A question is raised regarding the relationship between the duty cycle of the square wave and the presence of odd harmonics.
  • Another participant mentions that the function f(x) = |sin(x)| contains only even harmonics, contrasting it with the square wave.

Areas of Agreement / Disagreement

Participants express differing views on the role of even harmonics and the influence of the duty cycle, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

Participants do not clarify the specific conditions under which the even harmonics are considered low or the implications of the duty cycle on harmonic content.

likephysics
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Why does a square wave contain only odd harmonics of the fundamental?
If the even harmonics are low, how low are they.
What happens to the even harmonics.
 
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Because the resulting function is odd. Even fundamental harmonics would be destructive.
 
likephysics said:
Why does a square wave contain only odd harmonics of the fundamental?
If the even harmonics are low, how low are they.
What happens to the even harmonics.

That's the Fourier expansion for a square wave:
\frac{4}{\pi}(sin(x) + sin(3x)/3 + sin (5x)/5 + ...)

The function f(x) = |sin(x)| has only even harmonics.
 
Does the duty cycle of the square wave have anything to do with the odd harmonics?
 

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