%分析 sin(pi/4*k)和 cos(pi/8*k)  (長度分別為8 和16 )的頻譜在8點和16點上的dft
k=0:7;
k2=0:15;
n=8;
n2=16;
x11=cos(pi.*k/4);

x22=sin(pi.*k2/8);
F_81=fft(x11);
F_82=fft(x11,16);
F_161=fft(x22,8);
F_162=fft(x22);
subplot(2,2,1);
stem(k/8,abs(F_81));
title('cos(pi/8*k)的8點DFT');
subplot(2,2,2);
stem(k2/16,abs(F_82));
xlabel('Normalized freqency');
title('cos(pi/8*k)的16點DFT');
subplot(2,2,3);
stem(k/8,abs(F_161));
title('sin(pi/4*k)的 8 點DFT');
subplot(2,2,4);
stem(k2/16,abs(F_162));
xlabel('Normalized freqency');
title('sin(pi/4*k)的 1 6 點DFT');