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Fourier-Series Approximation of a Square Wave

rotate the linkage

select a joint

Black

Orange

Green

Blue

Red

A square wave with amplitude 1 and wavelength

can be approximated by the Fourier expansion

∞

∑

n=1,3,5,…

nπ

sin

2πn

a sum of sines with amplitudes

nπ

and frequencies

This Demonstration uses an open five-bar linkage to represent Fourier approximations of increasing accuracy. The

bar of the linkage has length

nπ

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.

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

Erik Mahieu

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