Fourfun

A system for automatic computations using Fourier expansions

This is a collection of functions named Fourfun that uses object-oriented programming in MATLAB. It can be used to quickly and accurately approximate periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax.

To get started, one must make a fourfun object. Fourfun objects can then be manipulated using the following functions: cos, diff, exp, int, integral, log, plot, roots, sin. See the comments for the required arguments for each function.

Here is a quick and simple example of how to make a fourfun object (a fourfun object is the approximation of a periodic function), find the roots of the fourfun, and then plot the results.

f=fourfun(@(x) cos(3*x));
g=roots(f);

hold on
plot(f,'r')
plot(g,zeros(1,length(g)),'.k')
hold off