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diff --git a/716/CH4/EX4.1/Solved_Ex_4_1.sce b/716/CH4/EX4.1/Solved_Ex_4_1.sce
new file mode 100755
index 000000000..295fa4a28
--- /dev/null
+++ b/716/CH4/EX4.1/Solved_Ex_4_1.sce
@@ -0,0 +1,104 @@
+//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=A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4)) ,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=A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4)) ,endfunction//redefining signal
+        //Evaluation of a0 & an
+        //Evaluation of a0:
+        a0=0;  //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=(A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4))).*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=A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4)) ,endfunction//redefining signal
+        //Evaluation of bn=>
+        y0=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=A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4)).*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);
+        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=A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4)) ,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=(A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4))).*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=f(t),x=A.*((t>-T/4 & t<T/4)+(t>-T & t<-3*T/4)+(t>3*T/4 & t<T))+(-A).*((t>-3*T/4&t<-T/4)+(t>T/4&t<3*T/4)) ,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  
+    end
+    y0=y1+y2;
+end
+
+xset('window',2);
+plot(t,y0);//x(t) signal till 8 harmonics
+xtitle('signal x(t) for 8 harmonics','time t','x(t)');
+\ No newline at end of file
diff --git a/716/CH4/EX4.10/Solved_Ex_4_10.sce b/716/CH4/EX4.10/Solved_Ex_4_10.sce
new file mode 100755
index 000000000..6de4a3b69
--- /dev/null
+++ b/716/CH4/EX4.10/Solved_Ex_4_10.sce
@@ -0,0 +1,103 @@
+//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=(2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & 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=(2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & 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=((2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & 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=(2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & t<T) ,endfunction//redefining signal
+        //Evaluation of bn=>
+        y0=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=((2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & 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);
+        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=(2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & t<T) ,endfunction//redefining signal
+        //Evaluation of a0,an & bn
+        //Evaluation of a0 & an:
+        a0=0;  //definite integral of 'f' from 0 to T/2
+        disp(a0,'a0');
+        disp('due to convergence,for even values of n,an=0');
+        disp('for even values of n,an=>');
+        y1=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=((2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & t<T)).*cos(n.*w0.*t) ,endfunction 
+        an=2*intg(0,T,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)*cos(n*w0*t)');
+        end
+            
+        //Evaluation of bn=>
+        y2=zeros(1,length(t));
+        disp('bn is 0 at even values');
+        for n=1:2:15                  //changing the end value of n,we can get more numbers of bn
+        function xn=f1(t),xn=((2*A/T*t+2*A).*(t>-T & t<-T/2)+(-2*A/T*t-A).*(t>-T/2 & t<0)+(2*A/T*t).*(t>0 & t<T/2)+(-2*A/T*t+A).*(t>T/2 & t<T)).*sin(n.*w0.*t) ,endfunction
+        bn=2*intg(0,T,f1)/T;
+        disp(n,'b');
+        disp(bn);
+        y2=y2+bn.*sin(n.*w0.*t);
+        xset('window',2);
+        subplot(2,4,(n+1)/2);
+        plot(t,y2);
+        xtitle('signal x(t) for few harmonics','time t','x(t)*sin(n*w0*t)');
+        end  
+    end
+    y0=y1+y2;
+end
+
+xset('window',3);
+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
diff --git a/716/CH4/EX4.13/Solved_Ex_4_13.sce b/716/CH4/EX4.13/Solved_Ex_4_13.sce
new file mode 100755
index 000000000..3680d18df
--- /dev/null
+++ b/716/CH4/EX4.13/Solved_Ex_4_13.sce
@@ -0,0 +1,25 @@
+//Determine the Fourier Transform of x(t)=1-t^2 for |t|<1 x(t)=0 for |t|>1
+clc;
+clear;
+T=8;
+t=-T:0.01:T
+w0=2*%pi/T;
+Dt=0.005;
+
+function x=f(t),x=(1-t^2).*(t>-1&t<1) ,endfunction
+x=f(t),x=(1-t^2).*(t>-1&t<1)
+plot(t,f);
+xlabel("time");
+ylabel("x(t)");
+
+K=4;
+k =0:(K/1000):K;
+W = k*w0/K;
+
+X=x*exp(-sqrt(-1)*t'*W)*Dt;
+xset('window',1);
+subplot(2,1,1)
+plot(W,abs(X));
+xtan=atan(imag(X)/real(X));
+subplot(2,1,2)
+plot(W,xtan);
+\ No newline at end of file
diff --git a/716/CH4/EX4.2.V/4_19_ExerciseV4_2.sce b/716/CH4/EX4.2.V/4_19_ExerciseV4_2.sce
new file mode 100755
index 000000000..f10d86bdd
--- /dev/null
+++ b/716/CH4/EX4.2.V/4_19_ExerciseV4_2.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-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & t<=T) ,endfunction//redefining signal
+        //Evaluation of a0 & an
+        //Evaluation of a0:       
+        a0=0;  //convergence gives a0=0
+        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-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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 xn=f1(t),xn=((-4*A/T*t-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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 xn=f1(t),xn=((-4*A/T*t-3*A).*(t>=-T & t<=-T/2)+(4*A/T*t+A).*(t>-T/2 & t<=0)+(-4*A/T*t+A).*(t>0 & t<=T/2)+(4*A/T*t-3*A).*(t>T/2 & 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
diff --git a/716/CH4/EX4.2/Solved_Ex_4_2.sce b/716/CH4/EX4.2/Solved_Ex_4_2.sce
new file mode 100755
index 000000000..3abe8b2ca
--- /dev/null
+++ b/716/CH4/EX4.2/Solved_Ex_4_2.sce
@@ -0,0 +1,104 @@
+//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=(2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0) ,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=(2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0) ,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=((2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0)).*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=(2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0) ,endfunction//redefining signal
+        //Evaluation of bn=>
+        y0=zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of bn
+        function x=f(t),x=(2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0) ,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);
+        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=(2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0) ,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=1:2:15                 //changing the end value of n,we can get more numbers of an
+        function xn=f1(t),xn=((2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0)).*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=((2*A/T*t).*(t>0 & t<=T/2)+(2*A/T*t+2*A).*(t>-T & t<=-T/2)+(-2*A/T*t+2*A).*(t>T/2 & t<T)+(-2*A/T*t).*(t>-T/2 & t<0)).*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  
+    end
+    y0=y1+y2;
+end
+
+xset('window',2);
+plot(t,y0);//x(t) signal till 8 harmonics
+xtitle('signal x(t) for 8 harmonics','time t','x(t)');
+\ No newline at end of file
diff --git a/716/CH4/EX4.21/Solved_Ex_4_21.sce b/716/CH4/EX4.21/Solved_Ex_4_21.sce
new file mode 100755
index 000000000..508154d16
--- /dev/null
+++ b/716/CH4/EX4.21/Solved_Ex_4_21.sce
@@ -0,0 +1,13 @@
+//Determine fourier transform of Given Signal and sketch magnitude and phase spectrum
+clc;
+clear;
+t=0:0.1:15;
+a=1;
+x=exp(-a*t).*(t>=0);
+X=dft(x,-1);
+Xmag=abs(X);
+subplot(1,2,1)
+plot(t,Xmag);
+xphase=atan(imag(X),real(X));
+subplot(1,2,2)
+plot(t,xphase)
+\ No newline at end of file
diff --git a/716/CH4/EX4.3/Solved_Ex_4_3.sce b/716/CH4/EX4.3/Solved_Ex_4_3.sce
new file mode 100755
index 000000000..3c4bd9a65
--- /dev/null
+++ b/716/CH4/EX4.3/Solved_Ex_4_3.sce
@@ -0,0 +1,104 @@
+//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=A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4) ,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=A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4) ,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=(A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4)).*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=A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4) ,endfunction//redefining signal
+        //Evaluation of bn=>
+        y0=zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of bn
+        function x=f(t),x=A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4) ,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);
+        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=A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4) ,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=(A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4)).*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=f(t),x=A.*(t>=-T/4 & t<=T/4)+A.*(t>=3*T/4 & t<=T)+A.*(t>=-T & t<=-3*T/4) ,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  
+    end
+    y0=y1+y2;
+end
+
+xset('window',2);
+plot(t,y0);//x(t) signal till 8 harmonics
+xtitle('signal x(t) for 8 harmonics','time t','x(t)');
+\ No newline at end of file
diff --git a/716/CH4/EX4.4/Solved_Ex_4_4.sce b/716/CH4/EX4.4/Solved_Ex_4_4.sce
new file mode 100755
index 000000000..15c699417
--- /dev/null
+++ b/716/CH4/EX4.4/Solved_Ex_4_4.sce
@@ -0,0 +1,113 @@
+//Solved_Ex.4.4->Determine the Trigonometric form of Fourier Series of the Full Wave Rectified sine wave
+clc;
+clear;
+T=8;//Defining Time Period
+A=2;//Defining Amplitude
+
+t=0:0.01:15;
+w0=2*%pi/T;
+
+function x=f(t),x=A.*abs(sin(t.*w0)) ,endfunction  //given full wave rectified continuous signal
+plot(t,f);
+xlabel("time");
+ylabel("x(t)");
+
+
+
+//Check if Even Signal,if yes,then bn=0
+if(f(t)==f(-1*t))
+    
+        disp('even');
+        disp('bn=0');
+        function x=f(t),x=A.*abs(sin(t.*w0)) ,endfunction  //given 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 odd values of n,a=0');
+        disp('for even values of n,an values are=>');
+        y0=a0/2+zeros(1,length(t));
+        for n=2:2:8                  //changing the end value of n,we can get more numbers of an
+        function xn=f1(t),xn=A.*abs(sin(t.*w0)).*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(2,2,n/2);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*cos(n*w0*t) for n=");
+        end
+
+        xset('window',2);
+        plot(t,y0);
+
+        xset('window',2);
+        plot(t,y0);
+    
+    else if(f(t)==(-1*f(-1*t)))
+    
+        disp('odd signal=>a0=an=0');
+        function x=f(t),x=A.*abs(sin(t.*w0)) ,endfunction //redefining signal
+        //Evaluation of bn=>
+        y0=zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of bn
+        function xn=f1(t),xn=A.*abs(sin(t.*w0)).*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);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*sin(n*w0*t) for n=");
+        end
+    
+    else
+    
+        disp('unknown');
+        function xn=f1(t),xn=A.*abs(sin(t.*w0)).*sin(n.*w0.*t) ,endfunction 
+        //Evaluation of a0,an & bn
+        //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:
+        y0=a0/2+zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of an
+        function xn=f1(t),xn=A.*abs(sin(t.*w0)).*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(2,2,n/2);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*cos(n*w0*t) for n=");
+        end
+    
+        //Evaluation of bn=>
+        y0=zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of bn
+        function xn=f1(t),xn=A.*abs(sin(t.*w0)).*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);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*sin(n*w0*t) for n=");
+        end
+    
+end
+end
+
+xset('window',2);
+plot(t,y0);//x(t) signal till 8 harmonics
+\ No newline at end of file
diff --git a/716/CH4/EX4.5/Solved_Ex_4_5.sce b/716/CH4/EX4.5/Solved_Ex_4_5.sce
new file mode 100755
index 000000000..8b781b140
--- /dev/null
+++ b/716/CH4/EX4.5/Solved_Ex_4_5.sce
@@ -0,0 +1,107 @@
+//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=A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & 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=A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & 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=(A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & 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=A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & t<T) ,endfunction//redefining signal
+        
+        //Evaluation of bn=>
+        disp('due to convergence,for all even values of n,bn=0');
+        disp('for odd values of n,bn values are=>');
+        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=(A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & 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=A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & 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=(A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & 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=f(t),x=A.*(t>-T & t<-T/2)+(-A).*(t>-T/2 & t<0)+A.*(t>0 & t<T/2)+(-A).*(t>T/2 & t<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
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
diff --git a/716/CH4/EX4.7/Solved_Ex_4_7.sce b/716/CH4/EX4.7/Solved_Ex_4_7.sce
new file mode 100755
index 000000000..2bbd1b9f8
--- /dev/null
+++ b/716/CH4/EX4.7/Solved_Ex_4_7.sce
@@ -0,0 +1,107 @@
+//Solved_Ex.4.7->Determine Trigonometric form of fourier Series of Given Signal
+clc;
+clear;
+T=8;//Defining Time Period
+A=2;//Defining Amplitude
+
+t=-3*T/2:0.01:3*T/2;
+w0=2*%pi/T;
+
+function x=f(t),x=(2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2) ,endfunction  //given continuous signal
+plot(t,f);
+xlabel("time");
+ylabel("x(t)");
+
+
+//Check if Even Signal,if yes,then bn=0
+if(f(t)==f(-1*t))
+    
+        disp('even');
+        disp('bn=0');
+        function x=f(t),x=(2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2) ,endfunction  //given 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:
+        y0=a0/2+zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of an
+        function xn=f1(t),xn=((2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2)).*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(2,2,n/2);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*cos(n*w0*t) for n=");
+        end
+
+        xset('window',2);
+        plot(t,y0);
+    
+    else if(f(t)==(-1*f(-1*t)))
+    
+        disp('odd signal=>a0=an=0');
+        function x=f(t),x=(2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2) ,endfunction //redefining signal
+        //Evaluation of bn=>
+        y0=zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of bn
+        function xn=f1(t),xn=((2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2)).*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);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*sin(n*w0*t) for n=");
+        end
+    
+    else
+    
+        disp('unknown');
+        function xn=f1(t),xn=((2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2)).*sin(n.*w0.*t) ,endfunction 
+        //Evaluation of a0,an & bn
+        //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:
+        y0=a0/2+zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of an
+        function xn=f1(t),xn=((2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2)).*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(2,2,n/2);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*cos(n*w0*t) for n=");
+        end
+    
+        //Evaluation of bn=>
+        y0=zeros(1,length(t));
+        for n=1:1:8                  //changing the end value of n,we can get more numbers of bn
+        function xn=f1(t),xn=((2*A/T*(t+T)).*(t>(-3*T/2)&t<(-1*T/2))+(2*A/T*t).*(t>(-1*T/2)&(t<T/2))+(2*A/T*(t-T)).*(t>T/2&t<3*T/2)).*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);
+        plot(t,y0);
+        xlabel("time");
+        ylabel("x(t)*sin(n*w0*t) for n=");
+        end
+    
+end
+end
+
+xset('window',2);
+plot(t,y0);//x(t) signal till 8 harmonics
+\ No newline at end of file
diff --git a/716/CH4/EX4.8/Solved_Ex_4_8.sce b/716/CH4/EX4.8/Solved_Ex_4_8.sce
new file mode 100755
index 000000000..17c7733bc
--- /dev/null
+++ b/716/CH4/EX4.8/Solved_Ex_4_8.sce
@@ -0,0 +1,90 @@
+//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=(A/T*t).*(t>0 & 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=(A/T*t).*(t>0 & 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=((A/T*t).*(t>0 & 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=(A/T*t).*(t>0 & t<T) ,endfunction//redefining signal
+        //Evaluation of bn=>
+        y0=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=((A/T*t).*(t>0 & 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);
+        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=(A/T*t).*(t>0 & t<T) ,endfunction//redefining signal
+        //Evaluation of a0,an & bn
+        //Evaluation of a0 & an:
+        a0=2*intg(0,T,f)/T;  //definite integral of 'f' from 0 to T/2
+        disp(a0,'a0');
+        disp('due to convergence,for all values of n,an=0');
+        y1=a0/2;
+            
+        //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 xn=f1(t),xn=((A/T*t).*(t>0 & t<T)).*sin(n.*w0.*t) ,endfunction
+        bn=2*intg(0,T,f1)/T;
+        disp(n,'b');
+        disp(bn);
+        y2=y2+bn.*sin(n.*w0.*t);
+        xset('window',1);
+        subplot(2,4,n);
+        plot(t,y2);
+        xtitle('signal x(t) for few harmonics','time t','x(t)*sin(n*w0*t)');
+        end  
+    end
+    y0=y1+y2;
+end
+
+xset('window',2);
+plot(t,y0);//x(t) signal till 8 harmonics
+xtitle('signal x(t) for 8 harmonics','time t','x(t)');
+\ No newline at end of file
diff --git a/716/CH4/EX4.9/Solved_Ex_4_9.sce b/716/CH4/EX4.9/Solved_Ex_4_9.sce
new file mode 100755
index 000000000..3fd3206d5
--- /dev/null
+++ b/716/CH4/EX4.9/Solved_Ex_4_9.sce
@@ -0,0 +1,103 @@
+//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=(sin(2*%pi/T*t)).*(t>0 & t<T/2) ,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=(sin(2*%pi/T*t)).*(t>0 & t<T/2) ,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=((sin(2*%pi/T*t)).*(t>0 & t<T/2)).*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=(sin(2*%pi/T*t)).*(t>0 & t<T/2) ,endfunction//redefining signal
+        //Evaluation of bn=>
+        y0=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=((sin(2*%pi/T*t)).*(t>0 & t<T/2)).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);
+        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=(sin(2*%pi/T*t)).*(t>0 & t<T/2) ,endfunction//redefining signal
+        //Evaluation of a0,an & bn
+        //Evaluation of a0 & an:
+        a0=2*intg(0,T,f)/T;  //definite integral of 'f' from 0 to T/2
+        disp(a0,'a0');
+        disp('due to convergence,for odd values of n,an=0');
+        disp('for even values of n,an=>');
+        y1=zeros(1,length(t));
+        for n=2:2:16                 //changing the end value of n,we can get more numbers of an
+        function xn=f1(t),xn=((sin(2*%pi/T*t)).*(t>0 & t<T/2)).*cos(n.*w0.*t) ,endfunction 
+        an=2*intg(0,T,f1)/T;
+        disp(n,'a');
+        disp(an);
+        y1=y1+an.*cos(n*w0.*t);
+        xset('window',1);
+        subplot(2,4,(n/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));
+        disp('bn is 0 at all the values except at n=1');
+        for n=1:1:1                  //changing the end value of n,we can get more numbers of bn
+        function xn=f1(t),xn=((sin(2*%pi/T*t)).*(t>0 & t<T/2)).*sin(n.*w0.*t) ,endfunction
+        bn=2*intg(0,T,f1)/T;
+        disp(n,'b');
+        disp(bn);
+        y2=y2+bn.*sin(n.*w0.*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  
+    end
+    y0=y1+y2+a0/2;
+end
+
+xset('window',3);
+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
author	priyanka	2015-06-24 15:03:17 +0530
committer	priyanka	2015-06-24 15:03:17 +0530
commit	b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch)
tree	ab291cffc65280e58ac82470ba63fbcca7805165 /716/CH4
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