Fourier Series Circles

Helpful and/or Insightful External Links:

  • Clicking here provides an intuitive explanation of the Fourier transform and provides an interface for creating your own Fourier circles like the ones below. 
  • Clicking here will take you to the original MATLAB code I used as my primary “backbone” for comprising the gifs below
  • Click here for example MATLAB code generating a gif animating the Fourier approximation for the square wave


Below are some MATLAB simulations illustrating the distinction between the individual sine functions comprising the Fourier series of a SISO (top diagram) vs. the summation of these sine functions (bottom diagram).  Both these scenarios are depicted as an”orbiting particle” about the unit circle on the left-hand side and are translated onto a 2D graph of  amplitude vs. angle. I have posted a link at the top of the page to the “backbone” code I used when creating these simulations. If you would like me to send you the script I compiled to generate these particular gifs, just leave you information in the the contact me section and I will be glad to send you them.

individual harmonics
Individual Harmonics
summed series
Summed Harmonics


  • The variable θ (units of degree) can be translated into units of time by mapping every revolution (θ = 360°) with some period of time T

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