Sawtooth2 Matlab Code

<source lang="matlab">

% % _-_,, ,, _-_- ,, % ( // || /, _  ; || ' % _|| /'\\ ||/\\ \\/\\ || __ < \, \\/\/\ ||/\ \\ \\/\\ _-_, % _|| || || || || || || ~||- - /-|| || | | ||_< || || || ||_. % || || || || || || || ||===|| (( || || | | || | || || || ~ || % -__-, \\,/ \\ |/ \\ \\ ( \_, | \/\\ \\/\\/ \\,\ \\ \\ \\ ,-_- % _/ ` % % John Hawkins % LNA % Sawtooth Wave Fourier Example % 12 Jan 2010

t=linspace(-1,1,1000);

x=t-floor(t);

figure

plot(t,x,'k')

hold on;

f=1/2*ones(1,numel(t));

for n=1:100

   Plus=j/(2*pi*n)*exp(j*2*pi*n*t);

   Minus=j/(2*pi*-n)*exp(j*2*pi*-n*t);

   f=f+Plus+Minus;

   plot(t,Plus+Minus+1/2);

   switch n

       case 1

           f1=f;

       case 3

           f3=f;

       case 5

           f5=f;

       case 10

           f10=f;

       case 50

           f50=f;

   end

end

plot(t,f,'r');

axis equal;

fontsize=20;

title({['Sawtooth Wave Constructed of First 100 Terms'],...

   ['of Fourier Series, Each Term Shown']},...

   'fontname','times','fontsize',fontsize)

xlabel('t'); ylabel('x');

figure

plot(t,f-x)

title('Error when x(t) is Truncated after 100 Terms',...

   'fontname','times','fontsize',fontsize)

xlabel('Error'); ylabel('t');

figure

plot(t,f1,t,f3,t,f5,t,f10,t,f50,t,f)

axis equal

title('Sawtooth Wave Constructed of First n Terms',...

   'fontname','times','fontsize',fontsize);

xlabel('t'); ylabel('x');

legend('n=1','3','5','10','50','100','location','northwest');

</source>