From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 716/CH4/EX4.6/Solved_Ex_4_6.sce | 106 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 106 insertions(+)
 create mode 100755 716/CH4/EX4.6/Solved_Ex_4_6.sce

(limited to '716/CH4/EX4.6')

diff --git a/716/CH4/EX4.6/Solved_Ex_4_6.sce b/716/CH4/EX4.6/Solved_Ex_4_6.sce
new file mode 100755
index 000000000..46e4a1fc7
--- /dev/null
+++ b/716/CH4/EX4.6/Solved_Ex_4_6.sce
@@ -0,0 +1,106 @@
+//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)');
\ No newline at end of file
-- 
cgit