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13 files changed, 609 insertions, 0 deletions

diff --git a/842/CH3/EX3.10/Example3_10.sce b/842/CH3/EX3.10/Example3_10.sce
new file mode 100755
index 000000000..1731694d7
--- /dev/null
+++ b/842/CH3/EX3.10/Example3_10.sce
@@ -0,0 +1,38 @@
+//clear//

+//Example3.10:DTFS of x[n] =sin(Won)

+clear;

+close;

+clc;

+n = 0:0.01:5;

+N = 5;

+Wo = 2*%pi/N;

+xn = sin(Wo*n);

+for k =0:N-2

+  C(k+1,:) = exp(-sqrt(-1)*Wo*n.*k);

+  a(k+1) = xn*C(k+1,:)'/length(n);

+  if(abs(a(k+1))<=0.01) 

+    a(k+1)=0;

+  end

+end

+a =a'

+a_conj = conj(a);

+ak = [a_conj($:-1:1),a(2:$)]

+k = -(N-2):(N-2);

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-8,-1;8,1];

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d3('gnn',k,-imag(ak),5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d3('gnn',N+k,-imag(ak),5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d3('gnn',-(N+k),-imag(ak($:-1:1)),5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('ak')

diff --git a/842/CH3/EX3.11/Example3_11.sce b/842/CH3/EX3.11/Example3_11.sce
new file mode 100755
index 000000000..b9ec1f2b7
--- /dev/null
+++ b/842/CH3/EX3.11/Example3_11.sce
@@ -0,0 +1,67 @@
+//clear//

+//Example3.11:DTFS of 

+//x[n] = 1+sin(2*%pi/N)n+3cos(2*%pi/N)n+cos[(4*%pi/N)n+%pi/2]

+clear;

+close;

+clc;

+N = 10;

+n = 0:0.01:N;

+Wo = 2*%pi/N;

+xn =ones(1,length(n))+sin(Wo*n)+3*cos(Wo*n)+cos(2*Wo*n+%pi/2);

+for k =0:N-2

+  C(k+1,:) = exp(-sqrt(-1)*Wo*n.*k);

+  a(k+1) = xn*C(k+1,:)'/length(n);

+  if(abs(a(k+1))<=0.1) 

+    a(k+1)=0;

+  end

+end

+a =a';

+a_conj =conj(a);

+ak = [a_conj($:-1:1),a(2:$)];

+Mag_ak = abs(ak);

+for i = 1:length(a)

+  Phase_ak(i) = atan(imag(ak(i))/(real(ak(i))+0.0001));

+end

+Phase_ak = Phase_ak'

+Phase_ak = [Phase_ak(1:$-1) -Phase_ak($:-1:1)];

+k = -(N-2):(N-2);

+//

+figure

+subplot(2,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',k,real(ak),5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('Real part of(ak)')

+xlabel('                                                       k')

+subplot(2,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',k,imag(ak),5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('imaginary part of(ak)')

+xlabel('                                                       k')

+//

+figure

+subplot(2,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',k,Mag_ak,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('abs(ak)')

+xlabel('                                                       k')

+subplot(2,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',k,Phase_ak,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('<(ak)')

+xlabel('                                                       k')

diff --git a/842/CH3/EX3.12/Example3_12.sce b/842/CH3/EX3.12/Example3_12.sce
new file mode 100755
index 000000000..1f50c5c13
--- /dev/null
+++ b/842/CH3/EX3.12/Example3_12.sce
@@ -0,0 +1,32 @@
+//clear//

+//Example3.12:DTFS coefficients of periodic square wave

+clear;

+close;

+clc;

+N = 10;

+N1 = 2;

+Wo = 2*%pi/N;

+xn = ones(1,length(N));

+n = -(2*N1+1):(2*N1+1);

+a(1) = (2*N1+1)/N;

+for k =1:2*N1

+  a(k+1) = sin((2*%pi*k*(N1+0.5))/N)/sin(%pi*k/N);

+  a(k+1) = a(k+1)/N;

+  if(abs(a(k+1))<=0.1)

+    a(k+1) =0;

+  end

+end

+a =a';

+a_conj =conj(a);

+ak = [a_conj($:-1:1),a(2:$)];

+k = -2*N1:2*N1;

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',k,real(ak),5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('Real part of(ak)')

+xlabel('                                                       k')

diff --git a/842/CH3/EX3.13/Example3_13.sce b/842/CH3/EX3.13/Example3_13.sce
new file mode 100755
index 000000000..9b58c2b6e
--- /dev/null
+++ b/842/CH3/EX3.13/Example3_13.sce
@@ -0,0 +1,63 @@
+//clear//

+//Example3.13:DTFS

+//Expression of periodic sequence using

+//the summation two different sequence

+clear;

+close;

+clc;

+N = 5;

+n = 0:N-1;

+x1 = [1,1,0,0,1];

+x1 = [x1($:-1:1) x1(2:$)]; // Square Wave x1[n]

+x2 = [1,1,1,1,1];

+x2 = [x2($:-1:1) x2(2:$)];//DC sequence of x2[n]

+x = x1+x2;//sum of x1[n] & x2[n]

+//Zeroth DTFS coefficient of dc sequence

+c(1) = 1;

+//Zeroth DTFS coefficient of square waveform

+b(1) = 3/5;

+//Zeroth DTFS coefficient of sum of x1[n] & x2[n]

+a(1) = b(1)+c(1);

+//

+Wo = 2*%pi/N;

+for k =1:N-1

+  a(k+1) = sin((3*%pi*k)/N)/sin(%pi*k/N);

+  a(k+1) = a(k+1)/N;

+  if(abs(a(k+1))<=0.1)

+    a(k+1) =0;

+  end

+end

+a =a';

+a_conj =conj(a);

+ak = [a_conj($:-1:1),a(2:$)];

+k = -(N-1):(N-1);

+n = -(N-1):(N-1);

+//

+figure

+subplot(3,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',n,x,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x[n]')

+xlabel('                                                       n')

+subplot(3,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',n,x1,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x1[n]')

+xlabel('                                                       n')

+subplot(3,1,3)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',n,x2,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x2[n]')

+xlabel('                                                       n')

diff --git a/842/CH3/EX3.14/Example3_14.sce b/842/CH3/EX3.14/Example3_14.sce
new file mode 100755
index 000000000..194af6bf5
--- /dev/null
+++ b/842/CH3/EX3.14/Example3_14.sce
@@ -0,0 +1,33 @@
+//clear//

+//Example3.14:DTFS

+//Finding x[n] using parseval's relation of DTFS

+clear;

+close;

+clc;

+N = 6;

+n = 0:N-1;

+a(1) = 1/3;

+a(2)=0;

+a(4)=0;

+a(5)=0;

+a1 = (1/6)*((-1)^n);

+x =0;

+for k = 0:N-2

+  if(k==2)

+    x = x+a1;

+  else

+    x =  x+a(k+1);

+  end

+end

+x = [x($:-1:1),x(2:$)];

+n = -(N-1):(N-1);

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',n,x,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x[n]')

+xlabel('                                                       n')

diff --git a/842/CH3/EX3.15/Example3_15.sce b/842/CH3/EX3.15/Example3_15.sce
new file mode 100755
index 000000000..36afd07e0
--- /dev/null
+++ b/842/CH3/EX3.15/Example3_15.sce
@@ -0,0 +1,26 @@
+//clear//

+//Example3.15:DTFS:Periodic Convolution Property

+clear;

+clc;

+close;

+x = [1,1,0,0,0,0,1];

+X = fft(x);

+W = X.*X;

+w = ifft(W);

+w = abs(w);

+for i =1:length(x)

+  if (abs(w(i))<=0.1)

+     w(i) = 0;

+   end

+end

+w = [w($:-1:1) w(2:$)];

+N = length(x);

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',[-(N-1):0,1:N-1],w,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('w[n]')

+xlabel('                                                       n')

diff --git a/842/CH3/EX3.2/Example3_2.sce b/842/CH3/EX3.2/Example3_2.sce
new file mode 100755
index 000000000..833cacfdf
--- /dev/null
+++ b/842/CH3/EX3.2/Example3_2.sce
@@ -0,0 +1,80 @@
+//clear//

+//Example 3.2:CTFS of a periodic signal x(t)

+//Expression of continuous time signal

+//using continuous time fourier series

+clear;

+close;

+clc;

+t = -3:0.01:3;

+//t1 = -%pi*4:(%pi*4)/100:%pi*4;

+//t2 =-%pi*6:(%pi*6)/100:%pi*6;

+xot = ones(1,length(t));

+x1t = (1/2)*cos(%pi*2*t);

+xot_x1t = xot+x1t;

+x2t = cos(%pi*4*t);

+xot_x1t_x2t = xot+x1t+x2t;

+x3t = (2/3)*cos(%pi*6*t);

+xt = xot+x1t+x2t+x3t;

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,0;2 4];

+plot(t,xot)

+ylabel('t')

+title('xot =1')

+//

+figure

+subplot(2,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,-3;2 4];

+plot(t,x1t)

+ylabel('t')

+title('x1(t) =1/2*cos(2*pi*t)')

+subplot(2,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,0;2 4];

+plot(t,xot_x1t)

+ylabel('t')

+title('xo(t)+x1(t)')

+//

+figure

+subplot(2,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,-2;4 2];

+plot(t,x2t)

+ylabel('t')

+title('x2(t) =cos(4*pi*t)')

+subplot(2,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,0;4 4];

+plot(t,xot_x1t_x2t)

+ylabel('t')

+title('xo(t)+x1(t)+x2(t)')

+//

+figure

+subplot(2,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,-3;4 3];

+plot(t,x3t)

+ylabel('t')

+title('x1(t) =2/3*cos(6*pi*t)')

+subplot(2,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-4,-3;4 3];

+plot(t,xt)

+ylabel('t')

+title('x(t)=xo(t)+x1(t)+x2(t)+x3(t)')

diff --git a/842/CH3/EX3.3/Example3_3.sce b/842/CH3/EX3.3/Example3_3.sce
new file mode 100755
index 000000000..68ce3d358
--- /dev/null
+++ b/842/CH3/EX3.3/Example3_3.sce
@@ -0,0 +1,19 @@
+//clear//

+//Example3.3:Continuous Time Fourier Series Coefficients of 

+//a periodic signal x(t) = sin(Wot)

+clear;

+close;

+clc;

+t = 0:0.01:1;

+T = 1;

+Wo = 2*%pi/T;

+xt = sin(Wo*t);

+for k =0:5

+  C(k+1,:) = exp(-sqrt(-1)*Wo*t.*k);

+  a(k+1) = xt*C(k+1,:)'/length(t);

+  if(abs(a(k+1))<=0.01) 

+    a(k+1)=0;

+  end

+end

+a =a';

+ak = [-a,a(2:$)];

diff --git a/842/CH3/EX3.4/Example3_4.sce b/842/CH3/EX3.4/Example3_4.sce
new file mode 100755
index 000000000..a058dd87e
--- /dev/null
+++ b/842/CH3/EX3.4/Example3_4.sce
@@ -0,0 +1,45 @@
+//clear//

+//Example3.4:CTFS coefficients of a periodic signal 

+//x(t) = 1+sin(Wot)+2cos(Wot)+cos(2Wot+%pi/4)

+clear;

+close;

+clc;

+t = 0:0.01:1;

+T = 1;

+Wo = 2*%pi/T;

+xt =ones(1,length(t))+sin(Wo*t)+2*cos(Wo*t)+cos(2*Wo*t+%pi/4);

+for k =0:5

+  C(k+1,:) = exp(-sqrt(-1)*Wo*t.*k);

+  a(k+1) = xt*C(k+1,:)'/length(t);

+  if(abs(a(k+1))<=0.1) 

+    a(k+1)=0;

+  end

+end

+a =a';

+a_conj =conj(a);

+ak = [a_conj($:-1:1),a(2:$)];

+Mag_ak = abs(ak);

+for i = 1:length(a)

+  Phase_ak(i) = atan(imag(ak(i))/(real(ak(i))+0.0001));

+end

+Phase_ak = Phase_ak'

+Phase_ak = [Phase_ak(1:$) -Phase_ak($-1:-1:1)];

+figure

+subplot(2,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',[-k:k],Mag_ak,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('abs(ak)')

+xlabel('                                                       k')

+subplot(2,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',[-k:k],Phase_ak,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('<(ak)')

+xlabel('                                                       k')

diff --git a/842/CH3/EX3.5/Example3_5.sce b/842/CH3/EX3.5/Example3_5.sce
new file mode 100755
index 000000000..f40a4b0f5
--- /dev/null
+++ b/842/CH3/EX3.5/Example3_5.sce
@@ -0,0 +1,46 @@
+//clear//

+//Example3.5:CTFS coefficients of a periodic signal 

+//x(t) = 1, |t|<T1, and 0, T1<|t|<T/2

+clear;

+close;

+clc;

+T =4;

+T1 = T/4;

+t = -T1:T1/100:T1;

+Wo = 2*%pi/T;

+xt =ones(1,length(t));

+//

+for k =0:5

+  C(k+1,:) = exp(-sqrt(-1)*Wo*t.*k);

+  a(k+1) = xt*C(k+1,:)'/length(t);

+  if(abs(a(k+1))<=0.1) 

+    a(k+1)=0;

+  end

+end

+a =a';

+a_conj = real(a(:))-sqrt(-1)*imag(a(:));

+ak = [a_conj($:-1:1)',a(2:$)];

+k = 0:5;

+k = [-k($:-1:1),k(2:$)];

+Spectrum_ak = (1/2)*real(ak);

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-2,0;2,2];

+plot2d(t,xt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x(t)')

+xlabel('                                                       t')

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+plot2d3('gnn',k,Spectrum_ak,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('abs(ak)')

+xlabel('                                                       k')

diff --git a/842/CH3/EX3.6/Example3_6.sce b/842/CH3/EX3.6/Example3_6.sce
new file mode 100755
index 000000000..02f7b0e66
--- /dev/null
+++ b/842/CH3/EX3.6/Example3_6.sce
@@ -0,0 +1,35 @@
+//clear//

+//Example3.6: Time Shift Property of CTFS

+clear;

+close;

+clc;

+T =4;

+T1 = T/2;

+t = 0:T1/100:T1;

+Wo = 2*%pi/T;

+gt =(1/2)*ones(1,length(t));

+a(1)=0; //k=0, ak =0

+d(1)=0;

+for k =1:5

+  a(k+1) = (sin(%pi*k/2)/(k*%pi));

+  if(abs(a(k+1))<=0.01)

+    a(k+1)=0;

+  end

+   d(k+1) = a(k+1)*exp(-sqrt(-1)*k*%pi/2);

+end

+k = 0:5

+disp('Fourier Series Coefficients of Square Wave')

+a

+disp('Fourier Series Coefficients of g(t)=x(t-1)-0.5')

+d

+//

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-1,-2;1,4];

+plot2d([-t($:-1:1),t(1:$)],[-gt,gt],5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('g(t)')

+xlabel('                                                       t')

diff --git a/842/CH3/EX3.7/Example3_7.sce b/842/CH3/EX3.7/Example3_7.sce
new file mode 100755
index 000000000..21bc9c5a0
--- /dev/null
+++ b/842/CH3/EX3.7/Example3_7.sce
@@ -0,0 +1,48 @@
+//clear//

+//Example3.7:Derivative Property of CTFS

+clear;

+clc;

+close;

+T =4;

+T1 = T/2;

+t = 0:T1/100:T1;

+xt = [t($:-1:1) t]/T1;

+gt =(1/2)*ones(1,length(t));

+e(1) = 1/2; //k =0, e0 = 1/2

+for k =1:5

+  a(k+1) = (sin(%pi*k/2)/(k*%pi));

+  if(abs(a(k+1))<=0.01)

+    a(k+1)=0;

+  end

+  d(k+1) = a(k+1)*exp(-sqrt(-1)*k*%pi/2);

+  e(k+1) = 2*d(k+1)/(sqrt(-1)*k*%pi);

+end

+k = 0:5

+disp('Fourier Series Coefficients of Square Wave')

+a

+disp('Fourier Series Coefficients of g(t)=x(t-1)-0.5')

+d

+disp('Fourier Series Coefficients of Triangular Wave')

+e

+//Plotting the time shifted square waveform

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-1,-2;1,2];

+plot2d([-t($:-1:1),t(1:$)],[-gt,gt],5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('g(t)')

+xlabel('                                                                          t')

+//Plotting the Triangular waveform

+figure

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-1,0;1,2];

+plot2d([-t($:-1:1),t(1:$)],xt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x(t)')

+xlabel('t')

diff --git a/842/CH3/EX3.8/Example3_8.sce b/842/CH3/EX3.8/Example3_8.sce
new file mode 100755
index 000000000..981eb80ed
--- /dev/null
+++ b/842/CH3/EX3.8/Example3_8.sce
@@ -0,0 +1,77 @@
+//clear//

+//Example3.8:Fourier Series Representation of Periodic Impulse Train

+clear;

+clc;

+close;

+T =4;

+T1 = T/4;

+t = [-T,0,T];

+xt = [1,1,1]; //Generation of Periodic train of Impulses

+t1 = -T1:T1/100:T1;

+gt = ones(1,length(t1));//Generation of periodic square wave

+t2 = [-T1,0,T1];

+qt = [1,0,-1];//Derivative of periodic square wave   

+Wo = 2*%pi/T;

+ak = 1/T;

+b(1) = 0;

+c(1) = 2*T1/T;

+for k =1:5

+  b(k+1) = ak*(exp(sqrt(-1)*k*Wo*T1)-exp(-sqrt(-1)*k*Wo*T1));

+  if(abs(b(k+1))<=0.1)

+    b(k+1) =0;

+  end

+  c(k+1) = b(k+1)/(sqrt(-1)*k*Wo);

+  if(abs(c(k+1))<=0.1)

+    c(k+1) =0;

+  end

+end

+k = 0:5

+disp('Fourier Series Coefficients of periodic Square Wave')

+disp(b)

+disp('Fourier Series Coefficients of derivative of periodic square wave')

+disp(c)

+//Plotting the periodic train of impulses

+figure

+subplot(3,1,1)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-6,0;6,2];

+plot2d3('gnn',t,xt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('x(t)')

+//Plotting the periodic square waveform

+subplot(3,1,2)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-6,0;6,2];

+plot2d(t1,gt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d(T+t1,gt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d(-T+t1,gt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('g(t)')

+//Plotting the periodic square waveform

+subplot(3,1,3)

+a = gca();

+a.y_location = "origin";

+a.x_location = "origin";

+a.data_bounds=[-6,-2;6,2];

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d3('gnn',t2,qt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d3('gnn',T+t2,qt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+plot2d3('gnn',-T+t2,qt,5)

+poly1 = a.children(1).children(1);

+poly1.thickness = 3; 

+title('q(t)')