Fourier-Series Approximation of a Square Wave
Fourier-Series Approximation of a Square Wave
A square wave with amplitude 1 and wavelength can be approximated by the Fourier expansion
λ
∞
∑
n=1,3,5,…
4
nπ
2πn
λ
a sum of sines with amplitudes and frequencies .
4
nπ
n
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.
th
n
4
nπ
n
The ordinates of the joints represent progressive approximations to the sum, as you can see by operating the time gauge.