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+//Example 3_8//
+//Fourier Series of half-wave rectifier output
+//Assume the period of the signal T=1
+t=-0.5:0.01:1;
+T=1;
+for i=1:length(t)
+if t(i)<T/2 then
+x(i)=sin(2*%pi*t(i));
+else
+x(i)=0;
+end
+end
+k=-10:10;
+for i=1:length(k)
+if k(i)==1 then
+ak(i)=1/(4*%i);
+elseif k(i)==-1
+ak(i)=-1/(4*%i);
+else
+ak(i)=(cos(k(i)*%pi/2)*exp(-k(i)*%pi/2*-%i))/(%pi-(%pi*k(i)*k(i)));
+end
+end
+disp("The fourier series coefficients are")
+disp(ak)
+disp("magnitude of Fourier series coefficient")
+disp(abs(ak))
+//Plotting frequency spectrum
+subplot(2,1,1)
+plot(k,abs(ak),'.');
+xtitle("Magnitude Spectrum","k","jakj");
+for i=1:length(k)
+if k(i)==0|k(i)==3|k(i)==-3|k(i)==-5|k(i)==5 then
+phase(i)=0;
+elseif k(i)==-1 then
+phase(i)=%pi/2;
+elseif k(i)==1 then
+phase(i)=-%pi/2;
+elseif k(i)== -2|k(i)==-4
+phase(i)=%pi;
+elseif k(i)==2|k(i)==4
+phase(i)=-%pi;
+end
+end