Fourier-Series Approximation of a Square Wave

A square wave with amplitude 1 and wavelength can be approximated by the Fourier expansion
a sum of sines with amplitudes and frequencies .
This Demonstration uses an open five-bar linkage to represent Fourier approximations of increasing accuracy. The bar of the linkage has length and rotates at angular speeds around its joint with the preceding bar.
The ordinates of the joints represent progressive approximations to the sum, as you can see by operating the time gauge.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshots 1 through 5 show the progressive approximations of the square wave using one through five bars of the linkage.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.