%function that plots the result of summing the first N terms of the Fourier
%series expansion for a function fx
function[] = plotfourier(N)

dx = .001;
L = 2;
x = -L:dx:L;
Nx = length(x);

fx = x/L; %actual function, here just linear from -1 to 1

a = zeros(1,N);
b = zeros(1,N);

a0 = (dx/L)*sum(fx);

fest = (a0/2)*ones(1,Nx);

for n=1:N
    b(n) = (dx/L)*sum(sin(n*pi*x/L).*fx);
    a(n) = (dx/L)*sum(cos(n*pi*x/L).*fx);
    
    fest = fest + b(n)*sin(n*pi*x/L);
    fest = fest + a(n)*cos(n*pi*x/L);
end

plot(x,fx,'r');
hold on;
plot(x,fest,'k');

legend('Actual','Estimate');
xlabel('x');
ylabel('f');
end