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diff --git a/3812/CH4/EX4.1/4_1.sce b/3812/CH4/EX4.1/4_1.sce
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+//example 4_1
+//determine the fourier series coefficient of the signal plot its magnitude and phase spectrum
+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')