Fourier series of Sawtooth wave

[code matlab]
% xN(t)=sum(ak*exp(j*2*pi*k*t)), k=-N:N
clear cla
N=[1,5,10,20];              % test value list
t=[-1:0.001:1];             % time range
xn=zeros(size(N,2),size(t,2));  % initialize value
for i=1:size(t,2)           % x(t) – Original Sawtooth wave
    if t(i) < 0
        xt(i)=-2*t(i)-1;
    else
        xt(i)=-2*t(i)+1;
    end
end
figure(1)
plot(t,xt)
grid on
title(‘Sawtooth wave’)
figure(2)
for i=1:4
    for k=1:N(i)            % when k=0, a0=0
        xn(i,:)=xn(i,:)+2*sin(2*pi*k*t)/(pi*k);
    end
    subplot(2,2,i)
    %hold on
    plot(t,xn(i,:))
    title(sprintf(‘N=%.d’,N(i)))
    grid on
    axis([-1 1 -1.5 1.5])
end
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