第一題：
clear all
N=32;
n=0:N-1;
xn=0.9.^n;
XK=fft(xn,N);
magXK=abs(XK);
phaXK=angle(XK);
XK1=fft(xn,2*N);
magXK1=abs(XK1);
phaXK1=angle(XK1);
subplot(3,1,1);
plot(n,xn);
xlabel('n');ylabel('x(n)');
title('x(n) N')
subplot(3,1,2);
k=0:length(magXK)-1;
stem(k,magXK,'.');
xlabel('k');ylabel('|X(k)|');
title('X(k)')
subplot(3,1,3);
k1=0:length(magXK1)-1;
stem(k1,magXK1,'.');
xlabel('k1');ylabel('|X(k)|');
title('X(k)')

第二題：
clear all
N=100;
n=0:N-1;
xn=cos(2*pi*n/N);
XK=fft(xn,N);
magXK=abs(XK);
phaXK=angle(XK);
XK1=fft(xn,N*2);
magXK1=abs(XK1);
phaXK1=angle(XK1);
XK2=fft(xn,N+2);
magXK2=abs(XK2);
phaXK2=angle(XK2);
subplot(4,1,1);
plot(n,xn);
xlabel('n');ylabel('x(n)');
title('x(n) N')
subplot(4,1,2);
k=0:length(magXK)-1;
stem(k,magXK,'.');
xlabel('k');ylabel('|X(k)|');
title('X(k)')
subplot(4,1,3);
k1=0:length(magXK1)-1;
stem(k1,magXK1,'.');
xlabel('k1');ylabel('|X(k)|');
title('X(k)')
subplot(4,1,4);
k2=0:length(magXK2)-1;
stem(k2,magXK2,'.');
xlabel('k2');ylabel('|X(k)|');
title('X(k)')


第三題：
clear all
N=32;
n=0:N-1;
xn=0.9*sin(2*pi*n/N)+0.6*sin(2*3*pi*n/N);
XK=fft(xn,N);
magXK=abs(XK);
phaXK=angle(XK);
subplot(2,1,1);
plot(n,xn);
xlabel('n');ylabel('x(n)');
title('x(n) N')
subplot(2,1,2);
k=0:length(magXK)-1;
stem(k,magXK,'.');
xlabel('k');ylabel('|X(k)|');
title('X(k)')

第四題:
clear all
N=32;
n=0:N-1;
xn=0.15*sin(pi*n/16)+sin(pi*n/8)-0.1*sin(3*pi*n/16);
XK=fft(xn,32);
magXK=abs(XK);
phaXK=angle(XK);
XK1=fft(xn,64);
magXK1=abs(XK1);
phaXK1=angle(XK1);
subplot(3,1,1);
plot(n,xn);
xlabel('n');ylabel('x(n)');
title('x(n) N')
subplot(3,1,2);
k=0:length(magXK)-1;
stem(k,magXK,'.');
xlabel('k');ylabel('|X(k)|');
title('X(k)')
subplot(3,1,3);
k1=0:length(magXK1)-1;
stem(k1,magXK1,'.');
xlabel('k1');ylabel('|X(k)|');
title('X(k)')