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+//Example 2.6

+

+clc;clear;close;

+A=1;T=2;

+w0=2*%pi/T;

+

+//Calculation of trignometric fourier series co-efficients

+a0=A/T*(integrate('-1','t',-T/2,0)+integrate('+1','t',0,T/2));

+for n=1:10

+a(1,n)=2*A/T*(integrate('-cos(n*w0*t)','t',-T/2,0)+integrate('+cos(n*w0*t)','t',0,T/2));

+b(1,n)=2*A/T*(integrate('-sin(n*w0*t)','t',-T/2,0)+integrate('+sin(n*w0*t)','t',0,T/2));

+end

+a=clean(a);b=clean(b);            //Function used to round small entities to zero

+

+//Calculation of exponential fourier series co-efficients

+function y=f(t),y=complex(cos(n*w0*t),-sin(n*w0*t)),endfunction;

+for n=-10:10

+c(1,n+11)=A/T*(-1*intc(-T/2,0,f)+intc(0,T/2,f));

+end

+c=clean(c);                      //Function used to round small entities to zero

+

+//Calculation of trignometric fourier series co-efficients from exponential fourie series coefficients

+a01=c(1);

+a1=2*real(c(12:21));

+b1=-2*imag(c(12:21));

+

+//Displaying fourier coefficients

+disp(T,'fundamental period T= ',A,'Assumption: Amplitude A= ');

+disp('Tignometric fourier series co-efficients:');

+disp(a0,'a0= ');disp(a,'an= ');disp(b,'bn= ');

+disp('Exponential fourier series co-efficients');

+disp(c(11),'c0= ');disp(c(12:21),'cn= ');disp(c(10:-1:1),'c-n= ');

+disp('Trignometric fourier series co-efficients from exponential coefficients:');

+disp(a01,'a0= ');disp(a1,'an= ');disp(b1,'bn= ');

+disp('The co-effifcients obtained are same by both methods')

+

+x=[-A*ones(1,50) A*ones(1,51)];

+t=-T/2:0.01*T:T/2;

+n=-10:10;

+subplot(311);plot(t,x);

+title('x(t)');xlabel('time t');

+subplot(312);plot2d3(a);

+title('Coefficients an');xlabel('n');

+subplot(313);plot2d3(b);

+title('Coefficients bn');xlabel('n');

+figure;

+subplot(311);plot(t,x);

+title('x(t)');xlabel('time t');

+subplot(312);plot2d3(n,abs(c));

+title('Magnitude of Coefficients |c|');xlabel('n');

+subplot(313);plot2d3(n,atan(c));

+title('Phase of Coefficients /_c');xlabel('n');
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