 # Amateur Extra: Sine Wave Odd Harmonics

## What type of wave is made up of a sine wave plus all of its odd harmonics? [E8A01]

A. A square wave
B. A sine wave
C. A cosine wave
D. A tangent wave

Well, the answer to this question is mathematically somewhat complex.  The answer is A. A square wave.

Rather than try and explain the formulation, which involves Fourier series, I think that this video I found on YouTube demonstrates the results perfectly.

So why would we want to do this?  Well, for “digital” anything, we need as close an approximation to a square wave as we can get, in order to represent those ones and zeros, or on and off states.  Since our oscillator circuits can’t on their own generate a square wave natively, only a sine wave, we need to take several different oscillator harmonics and combine them.  Just like in the above video.

If you’re really interested, here’s a great explanation, math and all: http://www.mathworks.com/help/matlab/examples/square-wave-from-sine-waves.html