initial commit / add all books

77 files changed, 967 insertions, 0 deletions

diff --git a/62/CH6/EX6.11/ex_6_11.png b/62/CH6/EX6.11/ex_6_11.png
new file mode 100755
index 000000000..f88d03b7c
--- /dev/null
+++ b/62/CH6/EX6.11/ex_6_11.png
diff --git a/62/CH6/EX6.11/ex_6_11.sce b/62/CH6/EX6.11/ex_6_11.sce
new file mode 100755
index 000000000..d96212f49
--- /dev/null
+++ b/62/CH6/EX6.11/ex_6_11.sce
@@ -0,0 +1,23 @@
+clear;

+close;

+clc;

+n=-10:10;

+a=2;

+for i=1:length(n)

+    if n(i)<=-1 then

+        x(i)=-2^n(i);

+    else

+        x(i)=0;

+    end

+end

+x=x';

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+title("x[n]")

+plot(n,x,'r.')

+w=-10:0.1:10;

+Xw=x*exp(-%i*n'*w);

+subplot(2,1,2)

+plot2d(w,Xw);

+title("X[w] fourier transform")

diff --git a/62/CH6/EX6.12/ex_6_12.png b/62/CH6/EX6.12/ex_6_12.png
new file mode 100755
index 000000000..09136f4c1
--- /dev/null
+++ b/62/CH6/EX6.12/ex_6_12.png
diff --git a/62/CH6/EX6.12/ex_6_12.sce b/62/CH6/EX6.12/ex_6_12.sce
new file mode 100755
index 000000000..2a342c711
--- /dev/null
+++ b/62/CH6/EX6.12/ex_6_12.sce
@@ -0,0 +1,23 @@
+clear;

+close;

+clc;

+n=-10:10;

+N=5;

+for i=1:length(n)

+    if n(i)>=0 & n(i)<=N then

+        x(i)=1;

+    else

+        x(i)=0;

+    end

+end

+x=x';

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+title("x[n]")

+plot(n,x,'r.')

+w=-10:0.1:10;

+Xw=x*exp(-%i*n'*w);

+subplot(2,1,2)

+plot2d(w,Xw);

+title("X[w] fourier transform")

diff --git a/62/CH6/EX6.14/ex_6_14.sce b/62/CH6/EX6.14/ex_6_14.sce
new file mode 100755
index 000000000..5ea8bd935
--- /dev/null
+++ b/62/CH6/EX6.14/ex_6_14.sce
@@ -0,0 +1,42 @@
+clear;

+close;

+clc;

+n=-10:10;

+N=4;

+for i=1:length(n)

+    if n(i)>=-N & n(i)<=N then

+        x(i)=1;

+    else

+        x(i)=0;

+    end

+end

+x=x';

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+title("x[n]")

+plot(n,x,'r.')

+w=-10:0.1:10;

+Xw=x*exp(-%i*n'*w);

+subplot(2,1,2)

+plot2d(w,Xw);

+title("X[w] fourier transform")

+N=8;

+for i=1:length(n)

+    if n(i)>=-N & n(i)<=N then

+        x(i)=1;

+    else

+        x(i)=0;

+    end

+end

+x=x';

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+title("x[n]")

+plot(n,x,'r.')

+w=-10:0.1:10;

+Xw=x'*exp(-%i*n'*w);

+subplot(2,1,2)

+plot2d(w,Xw);

+title("X[w] fourier transform")

diff --git a/62/CH6/EX6.14/ex_6_14a.png b/62/CH6/EX6.14/ex_6_14a.png
new file mode 100755
index 000000000..8d0b4110d
--- /dev/null
+++ b/62/CH6/EX6.14/ex_6_14a.png
diff --git a/62/CH6/EX6.14/ex_6_14b.png b/62/CH6/EX6.14/ex_6_14b.png
new file mode 100755
index 000000000..e66691812
--- /dev/null
+++ b/62/CH6/EX6.14/ex_6_14b.png
diff --git a/62/CH6/EX6.15/ex_6_15.png b/62/CH6/EX6.15/ex_6_15.png
new file mode 100755
index 000000000..2541ac14a
--- /dev/null
+++ b/62/CH6/EX6.15/ex_6_15.png
diff --git a/62/CH6/EX6.15/ex_6_15.sce b/62/CH6/EX6.15/ex_6_15.sce
new file mode 100755
index 000000000..d033fbc3a
--- /dev/null
+++ b/62/CH6/EX6.15/ex_6_15.sce
@@ -0,0 +1,26 @@
+clear;

+close;

+clc;

+W=%pi/4;

+w=-10:0.1:10;

+for i=1:length(w)

+    if (w(i)>=-2*%pi-W & w(i)<=-2*%pi+W)  then

+   X(i)=1;

+elseif (w(i)>=-W & w(i)<=W)

+    X(i)=1;

+elseif (w(i)>=2*%pi-W & w(i)<=2*%pi+W)

+    X(i)=1;

+else

+    X(i)=0;

+    end

+end

+figure

+subplot(2,1,1)

+plot(w,X);

+title("X[w]");

+n=-15:15;

+x=X'*exp(-%i*w'*n);

+subplot(2,1,2)

+plot2d3(n,x);

+plot(n,x,'r.')

+title("x[n] inverse fourier transform")

diff --git a/62/CH6/EX6.17/ex_6_17.png b/62/CH6/EX6.17/ex_6_17.png
new file mode 100755
index 000000000..51e08a5e9
--- /dev/null
+++ b/62/CH6/EX6.17/ex_6_17.png
diff --git a/62/CH6/EX6.17/ex_6_17.sce b/62/CH6/EX6.17/ex_6_17.sce
new file mode 100755
index 000000000..7e1dc069b
--- /dev/null
+++ b/62/CH6/EX6.17/ex_6_17.sce
@@ -0,0 +1,23 @@
+clear;

+close;

+clc;

+w=-5:0.01:5;

+W0=2;

+for i=1:length(w)

+    if w(i)==W0 then

+        delta(i)=2*%pi;

+    else 

+        delta(i)=0;

+    end

+end

+figure

+subplot(2,1,1)

+plot(w,delta);

+title('2*%pi*delta(w-w0)')

+//by shifting property

+n=-10:10;

+x=%e^-%i*W0*n;

+subplot(2,1,2)

+plot2d3(n,abs(x))

+plot(n,abs(x),'r.')

+title('x[n]')
\ No newline at end of file
diff --git a/62/CH6/EX6.18/ex_6_18.png b/62/CH6/EX6.18/ex_6_18.png
new file mode 100755
index 000000000..b3d8f5204
--- /dev/null
+++ b/62/CH6/EX6.18/ex_6_18.png
diff --git a/62/CH6/EX6.18/ex_6_18.sce b/62/CH6/EX6.18/ex_6_18.sce
new file mode 100755
index 000000000..883152187
--- /dev/null
+++ b/62/CH6/EX6.18/ex_6_18.sce
@@ -0,0 +1,22 @@
+clear;

+close;

+clc;

+n=-10:10;

+x=ones(1,length(n));

+figure

+subplot(2,1,1)

+plot2d3(n,x)

+plot(n,x,'r.')

+xtitle('x[n]','n')

+w=-5:0.01:5;

+for i=1:length(w)

+    if w(i)==0 then

+        delta(i)=1;

+    else 

+        delta(i)=0;

+    end

+end

+Xw=2*%pi*delta';

+subplot(2,1,2)

+plot(w,Xw);

+xtitle('X(w)','w')
\ No newline at end of file
diff --git a/62/CH6/EX6.19/ex_6_19.png b/62/CH6/EX6.19/ex_6_19.png
new file mode 100755
index 000000000..fc036da79
--- /dev/null
+++ b/62/CH6/EX6.19/ex_6_19.png
diff --git a/62/CH6/EX6.19/ex_6_19.sce b/62/CH6/EX6.19/ex_6_19.sce
new file mode 100755
index 000000000..1fb830a86
--- /dev/null
+++ b/62/CH6/EX6.19/ex_6_19.sce
@@ -0,0 +1,26 @@
+clear;

+close;

+clc;

+n=-10:10;

+W0=1;

+x=cos(W0*n);

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+title("x[n]")

+plot(n,x,'r.')

+//cos(W0*n)=1/2*(e^-%j*W0*n+e^%j*W0*n)

+w=-5:0.01:5;

+for i=1:length(w)

+    if w(i)==W0 then

+        deltaW0(i)=1;

+    else 

+        deltaW0(i)=0;

+    end

+end

+delta_W0=deltaW0($:-1:1);

+//by frequency shifting property

+Xw=1/2*[deltaW0+delta_W0];

+subplot(2,1,2)

+plot2d(w,Xw);

+title("X[w] fourier transform")

diff --git a/62/CH6/EX6.22/ex_6_22.sce b/62/CH6/EX6.22/ex_6_22.sce
new file mode 100755
index 000000000..726ed7db6
--- /dev/null
+++ b/62/CH6/EX6.22/ex_6_22.sce
@@ -0,0 +1,46 @@
+clear;

+close;

+clc;

+n=-10:10;

+N=2;

+for i=1:length(n)

+    if n(i)>=-N & n(i)<=N then

+        x(i)=1;

+    else

+        x(i)=0;

+    end

+end

+x=x';

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+title("x[n]")

+plot(n,x,'r.')

+w=-10:0.1:10;

+Xw=x*exp(-%i*n'*w);

+subplot(2,1,2)

+plot2d(w,Xw);

+title("X[w] fourier transform")

+//time scaled sequence x2[n]

+n2=-20:2:20;

+figure

+subplot(2,1,1)

+plot2d3(n2,x);

+title("x2[n]")

+plot(n2,x,'r.')

+w2=-5:0.05:5;

+subplot(2,1,2)

+plot2d(w2,Xw);

+title("X2[w] fourier transform")

+//time scaled sequence x3[n]

+n3=-30:3:30;

+figure

+subplot(2,1,1)

+plot2d3(n3,x);

+title("x3[n]")

+plot(n3,x,'r.')

+w3=w/3;

+subplot(2,1,2)

+plot2d(w3,Xw);

+title("X3[w] fourier transform")

+

diff --git a/62/CH6/EX6.22/ex_6_22_1.png b/62/CH6/EX6.22/ex_6_22_1.png
new file mode 100755
index 000000000..1f683e54a
--- /dev/null
+++ b/62/CH6/EX6.22/ex_6_22_1.png
diff --git a/62/CH6/EX6.22/ex_6_22_2_5.png b/62/CH6/EX6.22/ex_6_22_2_5.png
new file mode 100755
index 000000000..ddefe2d02
--- /dev/null
+++ b/62/CH6/EX6.22/ex_6_22_2_5.png
diff --git a/62/CH6/EX6.25/ex_6_25.png b/62/CH6/EX6.25/ex_6_25.png
new file mode 100755
index 000000000..7bd911e36
--- /dev/null
+++ b/62/CH6/EX6.25/ex_6_25.png
diff --git a/62/CH6/EX6.25/ex_6_25.sce b/62/CH6/EX6.25/ex_6_25.sce
new file mode 100755
index 000000000..fe8584632
--- /dev/null
+++ b/62/CH6/EX6.25/ex_6_25.sce
@@ -0,0 +1,14 @@
+clear;

+close;

+clc;

+a=0.7;

+n=-10:10;

+disp("X(w)=1/(1-a*e^(%i*w))^2=[1/(1-a*e^(%i*w))]*[1/(1-a*e^(%i*w))]");

+disp("we know a^n*u[n] <--> 1/(1-a*e^(%i*w))  ")

+//therefore by convolution property

+xpartial=[zeros(1,find(n==0)-1) a^n(find(n==0):$)];

+x=convol(xpartial,xpartial);

+n1=-20:20;

+plot2d3(n1,x);

+plot(n1,x,'r.');

+xtitle('x[n]','n')
\ No newline at end of file
diff --git a/62/CH6/EX6.28/ex_6_28.sce b/62/CH6/EX6.28/ex_6_28.sce
new file mode 100755
index 000000000..4360e6819
--- /dev/null
+++ b/62/CH6/EX6.28/ex_6_28.sce
@@ -0,0 +1,26 @@
+clear;

+close;

+clc;

+n=-10:10; 

+x=[zeros(1,find(n==0)-1) ones(1,length(n)-find(n==0)+1)];

+plot2d3(n,x)

+plot(n,x,'r.')

+xtitle('x[n]','n')

+figure

+w=-2:2;

+Xw=x*exp(-%i*n'*w);

+subplot(2,1,1)

+plot2d(w,real(Xw));

+xtitle('U[w] fourier transform','w')

+for i=1:length(w)

+    if w(i)==0 then

+        delta(i)=1;

+    else 

+        delta(i)=0;

+    end

+end

+Xwproof=%pi*delta'+ones(1,length(w))./(1-%e^(-%i*w));

+subplot(2,1,2)

+plot(w,Xwproof)

+xtitle('%pi*delta+1/(1-e^i*w','w')

+disp("it can be seen that both the figures are approximately same hence          X(w)=%pi*delta+1/(1-e^i*w");
\ No newline at end of file
diff --git a/62/CH6/EX6.28/ex_6_28_1.png b/62/CH6/EX6.28/ex_6_28_1.png
new file mode 100755
index 000000000..3f151b453
--- /dev/null
+++ b/62/CH6/EX6.28/ex_6_28_1.png
diff --git a/62/CH6/EX6.28/ex_6_28_2.png b/62/CH6/EX6.28/ex_6_28_2.png
new file mode 100755
index 000000000..f1bcb3553
--- /dev/null
+++ b/62/CH6/EX6.28/ex_6_28_2.png
diff --git a/62/CH6/EX6.3/ex_6_3.png b/62/CH6/EX6.3/ex_6_3.png
new file mode 100755
index 000000000..ebbd81e08
--- /dev/null
+++ b/62/CH6/EX6.3/ex_6_3.png
diff --git a/62/CH6/EX6.3/ex_6_3.sce b/62/CH6/EX6.3/ex_6_3.sce
new file mode 100755
index 000000000..878b45026
--- /dev/null
+++ b/62/CH6/EX6.3/ex_6_3.sce
@@ -0,0 +1,20 @@
+clear;

+close;

+clc;

+w0=2*%pi/4;//%pi/2

+N0=4;

+n=-8:7;

+y=0:3;

+x=[];

+for i=1:length(n)/4

+    x=[x y];

+end

+plot2d3(n,x');

+plot(n,x','r.')

+xtitle('x[n]','n')

+for k=0:3

+    c(k+1)=0;

+    for n=0:3

+       c(k+1)=c(k+1)+ (1/4)*(y(n+1))*(-%i)^(k*n);

+    end

+end

diff --git a/62/CH6/EX6.31/ex_6_31.png b/62/CH6/EX6.31/ex_6_31.png
new file mode 100755
index 000000000..875f31620
--- /dev/null
+++ b/62/CH6/EX6.31/ex_6_31.png
diff --git a/62/CH6/EX6.31/ex_6_31.sce b/62/CH6/EX6.31/ex_6_31.sce
new file mode 100755
index 000000000..182b07f70
--- /dev/null
+++ b/62/CH6/EX6.31/ex_6_31.sce
@@ -0,0 +1,18 @@
+clear;

+clc;

+close;

+disp("y[n]-3/4y[n-1]+1/8y[n-2]=x[n]");

+disp("taking fourier transform on both sides");

+disp("H(w)=Y(w)/X(w)=1/(1-(3/4)*e^(-j*w)+(1/8)*e^(-j*2*w))");

+w=-10:0.1:10;

+Hw=ones(1,length(w))./(1-(3/4)*%e^(-%i*w)+(1/8)*%e^(-%i*2*w));

+figure

+subplot(2,1,1)

+plot(w,Hw);

+xtitle('H(w)','w')

+n=-10:10;

+h=(1/(2*%pi))*Hw*exp(%i*w'*n);

+subplot(2,1,2)

+plot2d3(n,h)

+plot(n,h,'r.')

+xtitle('h[n]','n')
\ No newline at end of file
diff --git a/62/CH6/EX6.32/ex_6_32.sce b/62/CH6/EX6.32/ex_6_32.sce
new file mode 100755
index 000000000..012b1cc02
--- /dev/null
+++ b/62/CH6/EX6.32/ex_6_32.sce
@@ -0,0 +1,29 @@
+clear;

+clc;

+close;

+disp("y[n]-1/2*y[n-1]=x[n]+1/2*x[n-1]");

+disp("taking fourier transform on both sides");

+disp("H(w)=Y(w)/X(w)=(1+1/2*e^-j*w)/(1-1/2*e^-j*w)");

+w=-10:0.1:10;

+Hw=(1+(1/2)*%e^(-%i*w))./(1-(1/2)*%e^(-%i*w));

+figure

+subplot(2,1,1)

+plot(w,Hw);

+xtitle('H(w)','w')

+n=-10:10;

+h=(1/(2*%pi))*Hw*exp(%i*w'*n);

+subplot(2,1,2)

+plot2d3(n,h)

+xtitle('h[n]','n')

+plot(n,h,'r.')

+x=cos(%pi*n/2);

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+xtitle('x[n]','n')

+plot(n,x,'r.')

+y=convol(x,h);

+subplot(2,1,2)

+plot2d3(n,y(11:31))

+xtitle('y[n]','n')

+plot(n,y(11:31),'r.')
\ No newline at end of file
diff --git a/62/CH6/EX6.32/ex_6_32_1.png b/62/CH6/EX6.32/ex_6_32_1.png
new file mode 100755
index 000000000..a5d997356
--- /dev/null
+++ b/62/CH6/EX6.32/ex_6_32_1.png
diff --git a/62/CH6/EX6.32/ex_6_32_2.png b/62/CH6/EX6.32/ex_6_32_2.png
new file mode 100755
index 000000000..0f1448e21
--- /dev/null
+++ b/62/CH6/EX6.32/ex_6_32_2.png
diff --git a/62/CH6/EX6.33/ex_6_33.sce b/62/CH6/EX6.33/ex_6_33.sce
new file mode 100755
index 000000000..f04c1649a
--- /dev/null
+++ b/62/CH6/EX6.33/ex_6_33.sce
@@ -0,0 +1,34 @@
+clear;

+clc;

+close;

+n=-20:19;

+h=sinc(%pi*n/4)/4;

+disp("it can be seen that h[n] is a filter that allows frequencies between       -%pi/4 and +%pi/4")

+disp("therefore only the dc part of x[n] is passed i.e c0")

+subplot(2,1,1)

+plot2d3(n,h);

+plot(n,h,'r.');

+xtitle('h[n]','n')

+w=-4:0.01:4;

+Hw=h*exp(-%i*n'*w);

+subplot(2,1,2)

+plot2d(w,Hw);

+title("H[w] fourier transform")

+T0=5;

+w0=%pi*2/5;

+z=[ones(1,3) zeros(1,2)];

+x=[];

+for i=1:length(n)/T0

+    x=[x z];

+end

+figure

+subplot(2,1,1)

+plot2d3(n,x);

+plot(n,x,'r.')

+xtitle('x[n]','n')

+c0= (1/5)*sum(z);

+y=ones(1,length(n))*c0;

+subplot(2,1,2)

+plot2d3(n,y);

+plot(n,y,'r.--')

+xtitle('y[n]','n')
\ No newline at end of file
diff --git a/62/CH6/EX6.33/ex_6_33_1.png b/62/CH6/EX6.33/ex_6_33_1.png
new file mode 100755
index 000000000..3690eea7b
--- /dev/null
+++ b/62/CH6/EX6.33/ex_6_33_1.png
diff --git a/62/CH6/EX6.33/ex_6_33_2.png b/62/CH6/EX6.33/ex_6_33_2.png
new file mode 100755
index 000000000..ba3ce0397
--- /dev/null
+++ b/62/CH6/EX6.33/ex_6_33_2.png
diff --git a/62/CH6/EX6.34/ex_6_34.sce b/62/CH6/EX6.34/ex_6_34.sce
new file mode 100755
index 000000000..d9a77324b
--- /dev/null
+++ b/62/CH6/EX6.34/ex_6_34.sce
@@ -0,0 +1,38 @@
+clear;

+clc;

+close;

+disp("given system is y[n]=x[n]+x[n-1]");

+disp("taking fourier transform H(w)=Y(w)/X(w)=1+e^-j*w");

+//for impulse response x[n]=delta[n]

+n=-10:10;

+for i=1:length(n)

+    if n(i)==0 then

+        delta1(i)=1;

+        delta2(i)=0;

+    elseif n(i)==1

+        delta2(i)=1;

+        delta1(i)=0

+    else 

+        delta1(i)=0;

+        delta2(i)=0

+    end

+end 

+h=delta1+delta2;

+plot2d3(n,h);

+plot(n,h,'r.')

+xtitle('h[n]','n')

+figure

+subplot(2,1,1)

+w=-3:0.01:3;

+Hw=1+%e^(-%i*w);

+plot(w,abs(Hw))

+xtitle('|H(w)|','w')

+subplot(2,1,2)

+a=gca();

+plot(w,phasemag(Hw)*%pi/180)

+xtitle('theta(H(w))','w')

+a.y_location="origin";

+//3-db bandwidth

+cutoff=find(round(100*abs(Hw))==round(100*max(abs(Hw))/sqrt(2)));

+threedb=w(cutoff(3));

+disp(threedb,"3db bandwidth=")
\ No newline at end of file
diff --git a/62/CH6/EX6.34/ex_6_34_1.png b/62/CH6/EX6.34/ex_6_34_1.png
new file mode 100755
index 000000000..cab499999
--- /dev/null
+++ b/62/CH6/EX6.34/ex_6_34_1.png
diff --git a/62/CH6/EX6.34/ex_6_34_2.png b/62/CH6/EX6.34/ex_6_34_2.png
new file mode 100755
index 000000000..2af5cd59e
--- /dev/null
+++ b/62/CH6/EX6.34/ex_6_34_2.png
diff --git a/62/CH6/EX6.35/ex_6_35.sce b/62/CH6/EX6.35/ex_6_35.sce
new file mode 100755
index 000000000..3961a8106
--- /dev/null
+++ b/62/CH6/EX6.35/ex_6_35.sce
@@ -0,0 +1,22 @@
+clear;

+clc;

+close;

+disp("given system is y[n]-a*y[n-1]=x[n]");

+disp("taking fourier transform H(w)=Y(w)/X(w)=1/(1-a*e^-j*w)");

+//impulse response 

+n=-10:10;

+w=-3:0.01:3;

+a=.5;

+Hw=ones(1,length(w))./(1-a*%e^(-%i*w));

+h=(1/2*%pi)*Hw*exp(%i*w'*n); 

+disp("impulse response is a^n*u[n]")

+plot2d3(n,h);

+plot(n,h,'r.')

+xtitle('h[n]','n')

+figure

+plot(w,abs(Hw),'r')

+a=0.9;

+Hw=ones(1,length(w))./(1-a*%e^(-%i*w));

+plot(w,abs(Hw),'b')

+xtitle('|H(w)|','w')

+legend(['a=0.5';'a=0.9']);
\ No newline at end of file
diff --git a/62/CH6/EX6.35/ex_6_35_1.png b/62/CH6/EX6.35/ex_6_35_1.png
new file mode 100755
index 000000000..4ea9ba4a8
--- /dev/null
+++ b/62/CH6/EX6.35/ex_6_35_1.png
diff --git a/62/CH6/EX6.35/ex_6_35_2.png b/62/CH6/EX6.35/ex_6_35_2.png
new file mode 100755
index 000000000..563f6791a
--- /dev/null
+++ b/62/CH6/EX6.35/ex_6_35_2.png
diff --git a/62/CH6/EX6.36/ex_6_36.png b/62/CH6/EX6.36/ex_6_36.png
new file mode 100755
index 000000000..33b9108a9
--- /dev/null
+++ b/62/CH6/EX6.36/ex_6_36.png
diff --git a/62/CH6/EX6.36/ex_6_36.sce b/62/CH6/EX6.36/ex_6_36.sce
new file mode 100755
index 000000000..674a42749
--- /dev/null
+++ b/62/CH6/EX6.36/ex_6_36.sce
@@ -0,0 +1,29 @@
+clear;

+clc;

+close;

+wLPF=-3:0.1:3;

+wc=1;

+for i=1:length(wLPF)

+    if wLPF(i)>-wc & wLPF(i)<wc then

+        HwLPF(i)=1;

+    else

+        HwLPF(i)=0;

+    end

+end

+subplot(2,1,1)

+plot(wLPF,HwLPF)

+a=gca()

+poly1=a.children.children;

+poly1.thickness=3;

+poly1.foreground=2;

+title("low pass filter")

+disp("given h[n]=(-1)^n * hLPF[n]=e^(j*%pi*n) * hLPF[n]");

+disp("by shifting property H(w)=HLPF(w-%pi)")

+w=wLPF+%pi;

+subplot(2,1,2)

+plot(w,HwLPF)

+a=gca()

+poly1=a.children.children;

+poly1.thickness=3;

+poly1.foreground=2;

+title("high pass filter")

diff --git a/62/CH6/EX6.38/ex_6_38.png b/62/CH6/EX6.38/ex_6_38.png
new file mode 100755
index 000000000..96cbc4c56
--- /dev/null
+++ b/62/CH6/EX6.38/ex_6_38.png
diff --git a/62/CH6/EX6.38/ex_6_38.sce b/62/CH6/EX6.38/ex_6_38.sce
new file mode 100755
index 000000000..9fafe5998
--- /dev/null
+++ b/62/CH6/EX6.38/ex_6_38.sce
@@ -0,0 +1,17 @@
+clear;

+clc;

+close;

+disp("given y[n]=x[n]+x[n-1]  this can be converted to high pass filter by      multiplying with (-1)^n")

+disp("then y[n]=x[n]-x[n-1] taking fourier transform");

+disp("H(w)=1-e^-j*w");

+w=-3:0.01:3;

+Hw=1-%e^(-%i*w);

+subplot(2,1,1)

+plot(w,abs(Hw));

+xtitle('|H(w)|','w')

+subplot(2,1,2)

+plot(w(1:find(w==0)-1),phasemag(Hw(1:find(w==0)-1))*%pi/180)

+a=gca();

+a.y_location="origin";

+plot(w(find(w==0)+1:$),phasemag(Hw(find(w==0)+1:$))*%pi/180)

+xtitle('phase(H(w))','w')

diff --git a/62/CH6/EX6.4/ex_6_4.sce b/62/CH6/EX6.4/ex_6_4.sce
new file mode 100755
index 000000000..afdcc7cff
--- /dev/null
+++ b/62/CH6/EX6.4/ex_6_4.sce
@@ -0,0 +1,26 @@
+clear;

+close;

+clc;

+T0=10;

+w0=%pi/5;

+y=[ones(1,5) zeros(1,5)];

+n=-20:19;

+x=[];

+for i=1:length(n)/T0

+    x=[x y];

+end

+plot2d3(n,x);

+plot(n,x,'r.')

+xtitle('x[n]','n')

+for k=0:9

+     c(k+1)=0;

+    for n=0:4

+       c(k+1)=c(k+1)+ (1/4)*(y(n+1))*(%e)^(%i*w0*k*n);

+    end

+end

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

+k=-9:9;

+figure

+plot2d3(k,abs(c));

+plot(k,abs(c),'r.--')

+xtitle('|ck|','k')
\ No newline at end of file
diff --git a/62/CH6/EX6.4/ex_6_4_1.png b/62/CH6/EX6.4/ex_6_4_1.png
new file mode 100755
index 000000000..b41e12415
--- /dev/null
+++ b/62/CH6/EX6.4/ex_6_4_1.png
diff --git a/62/CH6/EX6.4/ex_6_4_2.png b/62/CH6/EX6.4/ex_6_4_2.png
new file mode 100755
index 000000000..77c4af945
--- /dev/null
+++ b/62/CH6/EX6.4/ex_6_4_2.png
diff --git a/62/CH6/EX6.40/ex_6_40.sce b/62/CH6/EX6.40/ex_6_40.sce
new file mode 100755
index 000000000..d2896ce5b
--- /dev/null
+++ b/62/CH6/EX6.40/ex_6_40.sce
@@ -0,0 +1,70 @@
+close;

+clc;

+clear;

+N=7;

+n=-4:12;

+for i=1:length(n)

+    if n(i)>=0 & n(i)<=(N-1)/2 then

+        h(i)=n(i);

+    elseif n(i)>=(N-1)/2 & n(i)<N

+        h(i)=-n(i)+(13+(-1)^N)/2;

+    else

+        h(i)=0;

+        

+    end

+end

+subplot(2,1,1)

+plot2d3(n,h)

+plot(n,h,'r.')

+title("N is odd")

+N=8;

+n=-4:12;

+for i=1:length(n)

+    if n(i)>=0 & n(i)<=(N-1)/2 then

+        h(i)=n(i);

+    elseif n(i)>=(N-1)/2 & n(i)<N

+        h(i)=-n(i)+(13+(-1)^N)/2;

+    else

+        h(i)=0;

+        

+    end

+end

+subplot(2,1,2)

+plot2d3(n,h)

+plot(n,h,'r.')

+title("N is even")

+disp("given h[n]=h[N-1-n] taking DFTF we get")

+disp("H(w)=H*(w) e^(-j*(N-1)*w)");

+disp("phase(w)=-1/2(N-1)*w");

+//h[n]=-h[N-1-n]

+N=7;

+n=-4:12;

+for i=1:length(n)

+    if n(i)>=0 & n(i)<N then

+        h(i)=n(i)-(N-1)/2;

+    else

+        h(i)=0;

+        

+    end

+end

+figure

+subplot(2,1,1)

+plot2d3(n,h)

+plot(n,h,'r.')

+title("N is odd")

+N=8;

+n=-4:12;

+for i=1:length(n)

+    if n(i)>=0 & n(i)<N then

+        h(i)=n(i)-(N-1)/2;

+      else

+        h(i)=0; 

+    end

+end

+subplot(2,1,2)

+plot2d3(n,h)

+plot(n,h,'r.')

+title("N is even")

+disp("given h[n]=-h[N-1-n] taking DFTF we get")

+disp("H(w)=-H*(w) e^(-j*(N-1)*w)");

+disp("phase(w)=%pi/2 - 1/2(N-1)*w")
\ No newline at end of file
diff --git a/62/CH6/EX6.40/ex_6_40a.png b/62/CH6/EX6.40/ex_6_40a.png
new file mode 100755
index 000000000..1b3c5a0b3
--- /dev/null
+++ b/62/CH6/EX6.40/ex_6_40a.png
diff --git a/62/CH6/EX6.40/ex_6_40b.png b/62/CH6/EX6.40/ex_6_40b.png
new file mode 100755
index 000000000..133a772c6
--- /dev/null
+++ b/62/CH6/EX6.40/ex_6_40b.png
diff --git a/62/CH6/EX6.41/ex_6_41.sce b/62/CH6/EX6.41/ex_6_41.sce
new file mode 100755
index 000000000..fa020ce0a
--- /dev/null
+++ b/62/CH6/EX6.41/ex_6_41.sce
@@ -0,0 +1,39 @@
+close;

+clc;

+clear;

+disp("given system y[n]=1/3*{x[n]+x[n-1]+x[n-2]}");

+disp("taking h[n]=1/3*{delta[n]+delta[n-1]+delta[n-2]}")

+n=-10:10;

+for i=1:length(n)

+    if n(i)==0 then

+        delta1(i)=1;

+        delta2(i)=0;

+        delta3(i)=0;

+    elseif n(i)==1

+        delta2(i)=1;

+        delta1(i)=0;

+        delta3(i)=0;

+    elseif n(i)==2

+        delta1(i)=0;

+        delta2(i)=0;

+        delta3(i)=1;

+    else 

+        delta1(i)=0;

+        delta2(i)=0;

+        delta3(i)=0;

+    end

+end 

+h={delta1+delta2+delta3}/3;

+plot2d3(n,h)

+plot(n,h,'r.')

+xtitle('h[n]','n')

+disp("taking DTFT H(w)={1+e^-j*w+e^-2*j*w}/3");

+w=-3:0.1:3;

+Hw={1+%e^(-%i*w)+%e^(-2*%i*w)}/3;

+figure

+subplot(2,1,1)

+plot(w,abs(Hw));

+xtitle('|H(w)|','w')

+subplot(2,1,2)

+plot(w,phasemag(Hw)*%pi/180);

+xtitle('phase(H(w))','w')
\ No newline at end of file
diff --git a/62/CH6/EX6.41/ex_6_41_1.png b/62/CH6/EX6.41/ex_6_41_1.png
new file mode 100755
index 000000000..6d1a325d1
--- /dev/null
+++ b/62/CH6/EX6.41/ex_6_41_1.png
diff --git a/62/CH6/EX6.41/ex_6_41_2.png b/62/CH6/EX6.41/ex_6_41_2.png
new file mode 100755
index 000000000..8b851d807
--- /dev/null
+++ b/62/CH6/EX6.41/ex_6_41_2.png
diff --git a/62/CH6/EX6.42/ex_6_42.sce b/62/CH6/EX6.42/ex_6_42.sce
new file mode 100755
index 000000000..6721dda4f
--- /dev/null
+++ b/62/CH6/EX6.42/ex_6_42.sce
@@ -0,0 +1,21 @@
+close;

+clc;

+clear;

+n=-10:10;

+h=[zeros(1,find(n==0)-1) 2 2 -2 -2 zeros(1,length(n)-find(n==0)-3)];

+plot2d3(n,h)

+plot(n,h,'r.')

+title("impulse response h[n]")

+disp("taking DTFT H(w)=sin(w/2)+sin(3*w/2)")

+w=-3:0.01:3;

+Hw=h*exp(-%i*n'*w);

+figure

+subplot(2,1,1)

+plot(w,abs(Hw)/4)

+xtitle('|H(w)|','w')

+subplot(2,1,2)

+plot(w(1:find(w==0)-1),phasemag(Hw(1:find(w==0)-1))*%pi/180)

+a=gca();

+a.y_location="origin";

+xtitle('phase(H(w))','w')

+plot(w(find(w==0)+1:$),phasemag(Hw(find(w==0)+1:$))*%pi/180)

diff --git a/62/CH6/EX6.42/ex_6_42_1.png b/62/CH6/EX6.42/ex_6_42_1.png
new file mode 100755
index 000000000..0064b572c
--- /dev/null
+++ b/62/CH6/EX6.42/ex_6_42_1.png
diff --git a/62/CH6/EX6.42/ex_6_42_2.png b/62/CH6/EX6.42/ex_6_42_2.png
new file mode 100755
index 000000000..ce9a2999d
--- /dev/null
+++ b/62/CH6/EX6.42/ex_6_42_2.png
diff --git a/62/CH6/EX6.43/ex_6_43.png b/62/CH6/EX6.43/ex_6_43.png
new file mode 100755
index 000000000..c24c2c3a0
--- /dev/null
+++ b/62/CH6/EX6.43/ex_6_43.png
diff --git a/62/CH6/EX6.43/ex_6_43.sce b/62/CH6/EX6.43/ex_6_43.sce
new file mode 100755
index 000000000..5b1e47bc0
--- /dev/null
+++ b/62/CH6/EX6.43/ex_6_43.sce
@@ -0,0 +1,29 @@
+close;

+clear;

+clc;

+disp("the system can be represented as Yc(s)=Xc(s)/(1+RCs)");

+disp("therefore Hc(s)=1/(1+RCs) hence hc(t)=e^-t*u(t) by frequency shifting     property")

+disp("therefore hd[n]=hc(t)=e^(-n*Ts)*u[n]");

+disp("taking z-transform Hd(z)=1/(1-e^(-n*Ts)*z^-1)");

+Ts=1;

+w=0:0.1:15;

+Hcw=ones(1,length(w))./(1+%i*w);

+subplot(2,1,1)

+plot(w,Hcw,'r')

+//z=%e^%i*w*Ts

+title("Ts=1")

+Hdw=ones(1,length(w))./(1-exp(-Ts-%i*w*Ts));

+plot(w,Hdw,'b')

+legend(["Hc(w)";"Hd(wTs)"])

+Ts=0.1;

+w=0:0.1:15;

+Hcw=ones(1,length(w))./(1+%i*w);

+subplot(2,1,2)

+plot(w,Hcw,'r')

+//z=%e^%i*w*Ts

+title("Ts=0.1")

+Hdw=ones(1,length(w))./(1-exp(-Ts-%i*w*Ts));

+//Hdw=ones(1,length(w))./(1+%e^(-2*Ts)-2*%e^(-Ts)*cos(w*Ts))^.5;

+plot(w,Hdw,'b')

+legend(["Hc(w)";"Hd(wTs)"])

+

diff --git a/62/CH6/EX6.44/ex_6_44.sce b/62/CH6/EX6.44/ex_6_44.sce
new file mode 100755
index 000000000..1ebbc0b2c
--- /dev/null
+++ b/62/CH6/EX6.44/ex_6_44.sce
@@ -0,0 +1,7 @@
+close;

+clear;

+clc;

+disp("the system is Hc(s)=1/(s+1)*(s+2)");

+disp("therefore hc(t)=(e^-t-e^-2*t)*u(t) by frequency shifting     property")

+disp("therefore hd[n]=hc(t)=(e^(-n*Ts)-e^(-2*n*Ts))*u[n]");

+disp("taking z-transform Hd(z)=1/(1-e^(-n*Ts)*z^-1)  -  1/(1-e^(-2*n*Ts)*z^-1");

diff --git a/62/CH6/EX6.45/ex_6_45.png b/62/CH6/EX6.45/ex_6_45.png
new file mode 100755
index 000000000..f5cfb749b
--- /dev/null
+++ b/62/CH6/EX6.45/ex_6_45.png
diff --git a/62/CH6/EX6.45/ex_6_45.sce b/62/CH6/EX6.45/ex_6_45.sce
new file mode 100755
index 000000000..32ee1943a
--- /dev/null
+++ b/62/CH6/EX6.45/ex_6_45.sce
@@ -0,0 +1,13 @@
+close;

+clear;

+clc;

+disp("Hc(s)=s")

+disp(" bilinear transformation s=2*(1-z^-1)/Ts*(1+z^-1)");

+disp("Hd(z)=2*(1-z^-1)/Ts*(1+z^-1)")

+//z=e^-j*w*Ts

+w=-1:0.01:1;

+Ts=2;

+Hdw=2*(1-%e^(-%i*w*Ts))./(1+%e^(-%i*w*Ts));

+//HdwTs=2*tan(w*Ts/2)/Ts;

+plot(w*Ts,imag(Hdw));

+xtitle('Hd(w)','w')
\ No newline at end of file
diff --git a/62/CH6/EX6.49/ex_6_49.sce b/62/CH6/EX6.49/ex_6_49.sce
new file mode 100755
index 000000000..b77ac4ead
--- /dev/null
+++ b/62/CH6/EX6.49/ex_6_49.sce
@@ -0,0 +1,56 @@
+close;

+clc;

+clear;

+n=0:10;

+N=8;

+for i=1:length(n)

+    if n(i)==0 then

+        delta(i)=1;

+    else

+        delta(i)=0;

+    end

+end

+x=delta';

+subplot(2,1,1)

+plot2d3(n,x);

+a=gca();

+plot(n,x,'r.')

+poly1=a.children.children;

+poly1.thickness=3;

+poly1.foreground=2;

+xtitle('x[n]','n')

+X=dft(x,-1);

+Y=X(1:find(n==N)-1);

+subplot(2,1,2)

+plot2d3(n,[Y' 0 0 0]);

+a=gca();

+plot(n,[Y' 0 0 0],'r.')

+poly1=a.children.children;

+poly1.thickness=3;

+poly1.foreground=2;

+xtitle('X[k]','k')

+for  i=1:length(n)

+    if n(i)>=0 & n(i)<N then

+        x(i)=1;

+    else

+        x(i)=0;

+    end

+    

+end

+figure 

+subplot(2,1,1)

+plot2d3(n,x);

+plot(n,x,'r.')

+a=gca();

+poly1=a.children.children;

+poly1.thickness=3;

+poly1.foreground=2;

+xtitle('x[n]','n')

+subplot(2,1,2)

+plot2d3(n,round(dft(x,-1)));

+plot(n,round(dft(x,-1)),'r.')

+a=gca();

+poly1=a.children.children;

+poly1.thickness=3;

+poly1.foreground=2;

+xtitle('X[k]','k')
\ No newline at end of file
diff --git a/62/CH6/EX6.49/ex_6_49_1.png b/62/CH6/EX6.49/ex_6_49_1.png
new file mode 100755
index 000000000..4ae3aa4a5
--- /dev/null
+++ b/62/CH6/EX6.49/ex_6_49_1.png
diff --git a/62/CH6/EX6.49/ex_6_49_2.png b/62/CH6/EX6.49/ex_6_49_2.png
new file mode 100755
index 000000000..d5f41e2c8
--- /dev/null
+++ b/62/CH6/EX6.49/ex_6_49_2.png
diff --git a/62/CH6/EX6.5/ex_6_5.sce b/62/CH6/EX6.5/ex_6_5.sce
new file mode 100755
index 000000000..cbad048e5
--- /dev/null
+++ b/62/CH6/EX6.5/ex_6_5.sce
@@ -0,0 +1,25 @@
+clear;

+close;

+clc;

+T0=4;

+w0=%pi/2;

+y=[1 0 0 0];

+n=-8:7;

+x=[];

+for i=1:length(n)/T0

+    x=[x y];

+end

+plot2d3(n,x);

+plot(n,x,'r.');

+xtitle('x[n]','n')

+for k=-9:9

+     c(k+10)=0;

+    for n=0:3

+       c(k+10)=c(k+10)+ (1/4)*(y(n+1))*(%e)^(%i*w0*k*n);

+    end

+end

+k=-9:9;

+figure

+plot2d3(k,abs(c));

+plot(k,c,'r.')

+xtitle('x[n]','n')
\ No newline at end of file
diff --git a/62/CH6/EX6.5/ex_6_5_1.png b/62/CH6/EX6.5/ex_6_5_1.png
new file mode 100755
index 000000000..f61f05726
--- /dev/null
+++ b/62/CH6/EX6.5/ex_6_5_1.png
diff --git a/62/CH6/EX6.5/ex_6_5_2.png b/62/CH6/EX6.5/ex_6_5_2.png
new file mode 100755
index 000000000..6cdbb79bc
--- /dev/null
+++ b/62/CH6/EX6.5/ex_6_5_2.png
diff --git a/62/CH6/EX6.50/ex_6_50.png b/62/CH6/EX6.50/ex_6_50.png
new file mode 100755
index 000000000..cb29ec0b2
--- /dev/null
+++ b/62/CH6/EX6.50/ex_6_50.png
diff --git a/62/CH6/EX6.50/ex_6_50.sce b/62/CH6/EX6.50/ex_6_50.sce
new file mode 100755
index 000000000..7234437d9
--- /dev/null
+++ b/62/CH6/EX6.50/ex_6_50.sce
@@ -0,0 +1,53 @@
+close;
+clc;
+clear;
+n=0:3;
+x=cos(%pi*n/2);
+subplot(4,1,1)
+plot2d3(n,x)
+xtitle('x[n]','n')
+a=gca();
+a.x_location="origin";
+a.y_location="right";
+poly1=a.children.children;
+poly1.thickness=3;
+poly1.foreground=2;
+plot(n,x,'r.')
+subplot(4,1,2)
+h=.5^n;
+plot2d3(n,h);
+xtitle('h[n]','n')
+a=gca();
+a.x_location="origin";
+a.y_location="right";
+poly1=a.children.children;
+poly1.thickness=3;
+poly1.foreground=2;
+plot(n,h,'r.')
+y=convol(x,h)
+subplot(4,1,3)
+plot2d3(n,y(1:4));
+xtitle('y[n]','n')
+plot(n,y(1:4),'r.')
+a=gca();
+a.x_location="origin";
+a.y_location="right";
+poly1=a.children.children;
+poly1.thickness=3;
+poly1.foreground=2;
+clear y;
+X=dft(x,-1);
+H=dft(h,-1);
+Y=H.*X;
+y=dft(Y,1);
+subplot(4,1,4)
+plot2d3(n,y);
+xtitle('y[n]','n')
+plot(n,y,'r.')
+a=gca();
+a.x_location="origin";
+a.y_location="right";
+poly1=a.children.children;
+poly1.thickness=3;
+poly1.foreground=2;
+plot(n,x,'r.')
diff --git a/62/CH6/EX6.55/ex_6_55.sce b/62/CH6/EX6.55/ex_6_55.sce
new file mode 100755
index 000000000..cd88ff496
--- /dev/null
+++ b/62/CH6/EX6.55/ex_6_55.sce
@@ -0,0 +1,5 @@
+x=[0 1 2 3];

+X=dft(x,-1);

+disp(X,"DFT is X(k)=")

+x=dft(X,1);

+disp(round(x),"IDFT is x[n]=")
\ No newline at end of file
diff --git a/62/CH6/EX6.56/ex_6_56.png b/62/CH6/EX6.56/ex_6_56.png
new file mode 100755
index 000000000..37057bc95
--- /dev/null
+++ b/62/CH6/EX6.56/ex_6_56.png
diff --git a/62/CH6/EX6.56/ex_6_56.sce b/62/CH6/EX6.56/ex_6_56.sce
new file mode 100755
index 000000000..69940fb52
--- /dev/null
+++ b/62/CH6/EX6.56/ex_6_56.sce
@@ -0,0 +1,15 @@
+clc;

+N=4;

+n=-10:10;

+x=[zeros(1,find(n==0)-1) rand(1,-find(n==0)+find(n==N)+1) zeros(1,length(n)-find(n==N))];

+plot2d3(n,x)

+nf=-5:0.5:5;

+figure

+subplot(2,1,1)

+plot2d3(ceil(nf),x);

+xtitle('f[n]','n')

+subplot(2,1,2)

+ng=nf-1/2;

+plot2d3(ceil(ng),x);

+xtitle('g[n]','n')

+disp("from the graphs it is visible that f[n]=g[n]=0 outside 0<=n<=N/2-1");
\ No newline at end of file
diff --git a/62/CH6/EX6.57/ex_6_57.sce b/62/CH6/EX6.57/ex_6_57.sce
new file mode 100755
index 000000000..631926af2
--- /dev/null
+++ b/62/CH6/EX6.57/ex_6_57.sce
@@ -0,0 +1,23 @@
+clear;

+close;

+clc;

+x=[1 1 -1 -1 -1 1 1 -1];

+N=8;

+n=0:7;

+k=0:N/2-1;

+WkN=exp(-%i*2*%pi*k/N);

+f=[];

+g=[];

+for i=1:length(n)

+    if modulo(n(i),2)==0 then

+        f=[f x(i)];

+    else

+        g=[g x(i)];

+    end

+end

+Fk=dft(f,-1);

+Gk=dft(g,-1);

+//Xk=Fk-WkN*Gk

+Xk=Fk-WkN'.*Gk;

+Xk=[Xk; Xk];

+disp(round(Xk))

diff --git a/62/CH6/EX6.59/ex_6_59.sce b/62/CH6/EX6.59/ex_6_59.sce
new file mode 100755
index 000000000..f1f73129c
--- /dev/null
+++ b/62/CH6/EX6.59/ex_6_59.sce
@@ -0,0 +1,22 @@
+clear;

+close;

+clc;

+x=[1 1 -1 -1 -1 1 1 -1];

+N=8;

+n=0:7;

+p=x(1:4)+x(5:8);

+k=0:N/2-1;

+WkN=exp(-%i*2*%pi*k/N);

+q=[x(1:4)-x(5:8)].*WkN;

+Pk=dft(p,-1);

+Qk=dft(q,-1);

+//X[2k]=P[k]  X[2k+1]=Q[k]

+for i=1:length(k)

+    if modulo(i,2)==0 then

+        Xk(i)=Qk(i/2);

+    else

+       Xk(i)=Pk(ceil((i)/2));

+    end

+end

+Xk=[Xk;Xk];

+disp(round(Xk));
\ No newline at end of file
diff --git a/62/CH6/EX6.6/ex_6_6.sce b/62/CH6/EX6.6/ex_6_6.sce
new file mode 100755
index 000000000..0285fc591
--- /dev/null
+++ b/62/CH6/EX6.6/ex_6_6.sce
@@ -0,0 +1,67 @@
+clear;

+close;

+clc;

+//cos(%pi*n/4)

+N0=8;

+w0=2*%pi/N0;

+n=-8:8;

+x=cos(%pi*n/4);

+subplot(2,1,1)

+xtitle('x[n]','n')

+plot2d3(n,x);

+plot(n,x,'r.');

+for k=-6:6

+     c(k+7)=0;

+    for n=0:7

+       c(k+7)=c(k+7)+ (1/8)*(x(n+1))*(%e)^(%i*w0*k*n);

+    end

+end

+k=-6:6;

+subplot(2,1,2)

+xtitle('|ck|','k')

+plot2d3(k,abs(c));

+plot(k,c,'r.')

+//cos(%pi*n/3)+sin(%pi*n/4)

+N0=24;

+w0=2*%pi/N0;

+n=-24:24;

+x=cos(%pi*n/3)+sin(%pi*n/4);

+figure

+subplot(2,1,1)

+xtitle('x[n]','n')

+plot2d3(n,x);

+plot(n,x,'r.--');

+for k=-24:24

+     c(k+25)=0;

+    for n=0:23

+       c(k+25)=c(k+25)+ (1/N0)*(x(n+1))*(%e)^(%i*w0*k*n);

+    end

+end

+k=-24:24;

+subplot(2,1,2)

+xtitle('|ck|','k')

+plot2d3(k,abs(c));

+plot(k,c,'r.')

+//[cos(%pi*n/8)]^2

+N0=8;

+w0=2*%pi/N0;

+n=-8:8;

+x=[cos(%pi*n/8)]^2;

+clear c;

+figure

+subplot(2,1,1)

+xtitle('x[n]','n')

+plot2d3(n,x);

+plot(n,x,'r.--');

+for k=-6:6

+     c(k+7)=0;

+    for n=0:7

+       c(k+7)=c(k+7)+ (1/N0)*(x(n+1))*(%e)^(%i*w0*k*n);

+    end

+end

+k=-6:6;

+subplot(2,1,2)

+xtitle('|ck|','k')

+plot2d3(k,abs(c));

+plot(k,c,'r.')

+disp("fourier series is x[n]=1/N0*sum(c(k)*e^%i*w0*n*k)");
\ No newline at end of file
diff --git a/62/CH6/EX6.6/ex_6_6_2.png b/62/CH6/EX6.6/ex_6_6_2.png
new file mode 100755
index 000000000..ebc3215ef
--- /dev/null
+++ b/62/CH6/EX6.6/ex_6_6_2.png
diff --git a/62/CH6/EX6.6/ex_6_6a.png b/62/CH6/EX6.6/ex_6_6a.png
new file mode 100755
index 000000000..d1b78c4cc
--- /dev/null
+++ b/62/CH6/EX6.6/ex_6_6a.png
diff --git a/62/CH6/EX6.61/ex_6_61.sce b/62/CH6/EX6.61/ex_6_61.sce
new file mode 100755
index 000000000..bc676c873
--- /dev/null
+++ b/62/CH6/EX6.61/ex_6_61.sce
@@ -0,0 +1,18 @@
+clear;

+close;

+clc;

+T1=10;

+wM=100;

+N=ceil(wM*T1/%pi);

+dw=2*wM/N;

+dt=%pi/wM;

+WN=exp(-%i*2*%pi/N);

+n=0:N-1;

+x=%e^-(n*dt);

+k=0:10;

+Xk=dt*x*exp(-%i*2*%pi*n'*k/N);

+disp(Xk(find(k==0)),Xk(find(k==1)),Xk(find(k==10)),"X[0] X[1] X[10] from X[k]")

+w=0:dw:10*dw;

+Xw=ones(1,length(w))./(%i*w+1);

+disp(Xw(find(w==0)),Xw(find(w==dw)),Xw(find(w==10*dw)),"X(0) X(dw) X(10*dw) from X(w)")

+disp("it can be seen that X[k] gives a good approximation to X(w)") 
\ No newline at end of file