MultiFunction Plotter: Fourier Series

Description| Fourier Series| Loan Repayments

We will use the multifunction plotter to show how a square wave can be represented as a sum of sine waves using the Fourier series. A square wave of amplitude of 2 and length 2L can be written as

Fourier Equation

(See this page for details of the equation.)

In the multifunction plotter, we key in the functions as follows:

Function 1 = 0.5-mod(int(x),2)

Function 2 = 2/pi()*sin(pi()*x) +
2/pi()*sin(pi()*x*3)/3 +

Function 3 = B5 + 2/pi()*sin(pi()*x*7)/7 +
2/pi()*sin(pi()*x*9)/9 +
2/pi()*sin(pi()*x*11)/11 +
2/pi()*sin(pi()*x*13)/13 +
2/pi()*sin(pi()*x*15)/15 +

The first function generates a square wave of amplitude 1, the second adds the first 3 terms of the Fourier expansion while the third adds the next 7 terms.

The result is shown below. The first equation is plotted in orange, the second in pink and the third in blue.

Fourier Series

Contribution from Visitors

Alexander Weiner from Germany used the Multifunction plotter tool and an Active-X control to create this file which allows the generation of the Fourier series plot with a large number of coefficients. He has kindly agreed to share his work on this site.

His file can be downloaded here.

A screen shot of his work is shown below, this shows a series with 100 coefficients. This is a nice illustration of Gibbs phenomenon, according to which the spikes at the discontinuities cannot be removed by increasing the number of coefficients.

Gibbs Phenomenon

Also See:

Discrete Fourier Transform

Filter Analysis and Simulation

FIR Filter Analysis