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//Determine the trigonometric form of fourier series of Given Signal
clc;
clear;
T=8;//Defining Time Period
A=2;//Defining Amplitude
t=-T:0.01:T;
w0=2*%pi/T;
function x=f(t),x=(4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T) ,endfunction //given continuous signal
plot(t,f);
xlabel("time");
ylabel("x(t)");
//Check if Signal is even or odd
if(f(t)==f(-1*t))
disp('even');
disp('bn=0');
function x=f(t),x=(4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T) ,endfunction//redefining signal
//Evaluation of a0 & an
//Evaluation of a0:
a0=4*intg(0,T/2,f)/T; //definite integral of 'f' from 0 to T/2
disp(a0,'a0');
//Evaluation of an:
disp('due to convergence,for all even values of n,an=0');
disp('for odd values of n,an values are=>');
y0=a0/2+zeros(1,length(t));
for n=1:2:15 //changing the end value of n,we can get more numbers of an
function xn=f1(t),xn=((4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T)).*cos(n.*w0.*t) ,endfunction
an=4*intg(0,T/2,f1)/T;
disp(n,'a');
disp(an);
y0=y0+an.*cos(n*w0.*t);
xset('window',1);
subplot(2,4,(n+1)/2);
plot(t,y0);
xtitle('signal x(t) for few harmonics','time t','x(t)');
end
else if(f(t)==(-1*f(-1*t)))
disp('odd signal=>a0=an=0');
function x=f(t),x=(4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T) ,endfunction//redefining signal
disp('due to convergence,for all even values of n,bn=0');
disp('for odd values of n,bn values are=>');
//Evaluation of bn=>
y0=zeros(1,length(t));
for n=1:2:15 //changing the end value of n,we can get more numbers of bn
function x=f1(t),x=((4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T)).*sin(n.*w0.*t) ,endfunction
bn=4*intg(0,T/2,f1)/T;
disp(n,'b');
disp(bn);
y0=y0+bn.*sin(w0.*n.*t);
xset('window',1);
subplot(2,4,(n+1)/2);
plot(t,y0);
xtitle('signal x(t) for few harmonics','time t','x(t)');
end
else
disp('neiher even nor odd');
function x=f(t),x=(4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T) ,endfunction//redefining signal
//Evaluation of a0,an & bn
//Evaluation of a0:
disp('due to convergence,for all even values of n,an=0');
disp('for odd values of n,an values are=>');
a0=0; //definite integral of 'f' from 0 to T/2
disp(a0,'a0');
//Evaluation of an:
y1=a0/2+zeros(1,length(t));
for n=1:2:13 //changing the end value of n,we can get more numbers of an
function xn=f1(t),xn=((4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T)).*cos(n.*w0.*t) ,endfunction
an=4*intg(0,T/2,f1)/T;
disp(n,'a');
disp(an);
y1=y1+an.*cos(n*w0.*t);
xset('window',1);
subplot(2,4,(n+1)/2);
plot(t,y1);
xtitle('signal x(t) for few harmonics','time t','x(t)*xcos(n*w0*t)');
end
//Evaluation of bn=>
y2=zeros(1,length(t));
for n=1:1:8 //changing the end value of n,we can get more numbers of bn
function x=f1(t),x=((4*A/T*t+4*A).*(t>=-T & t<=-3*T/4)+(-4*A/T*t-2*A).*(t>-3*T/4 & t<=-T/4)+(4*A/T*t).*(t>-T/4 & t<=T/4)+(-4*A/T*t+2*A).*(t>T/4 & t<=3*T/4)+(4*A/T*t-4*A).*(t>3*T/4 & t<=T)).*sin(n.*w0.*t) ,endfunction
bn=4*intg(0,T/2,f1)/T;
disp(n,'b');
disp(bn);
y2=y2+bn.*sin(w0.*n.*t);
xset('window',2);
subplot(2,4,n);
plot(t,y2);
xtitle('signal x(t) for few harmonics','time t','x(t)*sin(n*w0*t)');
end
y0=y1+y2;
end
end
xset('window',2);
plot(t,y0);//x(t) signal till 15 harmonics
xtitle('signal x(t) for 15 harmonics','time t','x(t)');
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