% ##################################################################################
% ##  Loesung:  DFT: Abbruchfehler, Unterabtastung                                ##
% ##################################################################################

kk08  =  0:7;
kk64  = 0:63;
x1_08 = sin(kk08*pi/8);    x1_64 = sin(kk64*pi/8);
x2_08 = sin(kk08*pi/2);    x2_64 = sin(kk64*pi/2);
x3_08 = sin(kk08*pi*3/2);  x3_64 = sin(kk64*pi*3/2);

figure; kk100=0:8/100:8; plot(kk100,sin(kk100*pi/8),':'); hold on;
stem(kk08,x1_08); axis([0 8 -1.2 1.2]); title('x1(k)=sin(k*pi/8), k=0...7');
figure;stem(kk08,abs(fft(x1_08))); axis([0 7 -1 6]); title('abs(X1(n)),n=0...7');
figure;stem(kk64,x1_64);axis([0 64 -1.2 1.2]);title('x1(k)=sin(k*pi/8),k=0...63');
figure;stem(kk64,abs(fft(x1_64)));axis([0 64 -1 40]);title('abs(X1(n)),n=0...63');
input('....Zum Fortfahren: RETURN druecken');

figure; kk100=0:8/100:8; plot(kk100,sin(kk100*pi/2),':'); hold on;
stem(kk08,x2_08); axis([0 8 -1.2 1.2]); title('x2(k)=sin(k*pi/2), k=0...7');
figure;stem(kk08,abs(fft(x2_08))); axis([0 7 -1 6]); title('abs(X2(n)),n=0...7');
figure;stem(kk64,x2_64);axis([0 64 -1.2 1.2]);title('x2(k)=sin(k*pi/2),k=0...63');
figure;stem(kk64,abs(fft(x2_64)));axis([0 64 -1 40]);title('abs(X2(n))),n=0...63');
input('....Zum Fortfahren: RETURN druecken');

figure; kk100=0:8/100:8; plot(kk100,sin(kk100*pi*3/2),':'); hold on;
stem(kk08,x3_08); axis([0 8 -1.2 1.2]); title('x3(k)=sin(k*pi*3/2), k=0...7');
figure;stem(kk08,abs(fft(x3_08))); axis([0 8 -1 6]); title('abs(X3(n)), n=0...7'); 
axis([0 7 -1 6]); 
figure;stem(kk64,x3_64);axis([0 64 -1.2 1.2]);title('x3(k)=sin(k*pi*3/2),k=0...63');
figure;stem(kk64,abs(fft(x3_64)));axis([0 64 -1 40]);title('abs(X3(n)),n=0...63');
% #####  EOF  #####