이라 하자. 이의 z-변환을 단위원에서 으로 샘플링하고 이의 시간 영역에 대한 영향을 조사해보자.

ex5_5.cem

/*   Chapter 5:   Example 5.5 
   Frequency-domain sampling
   x(n)=(0.7)^n * u(n)   X(z)=z/(z-0.7); |z|>0.7*/
 
subplot(1,1,1)//
N = 5;
k = 0:N-1:1;
wk = 2*pi*k/N;
zk = exp(j*wk);
Xk = (zk)./(zk-0.7);
xn = real(invdfs(Xk,N));
xtilde = xn'* ones(1,8); xtilde = (xtilde(:))';
subplot(2,2,1); stem(0:39,xtilde,"-");
xtitle("n"); ytitle("xtilde(n)"); title("N=5")//
N = 10;
k = 0:N-1:1;
wk = 2*pi*k/N;
zk = exp(j*wk);
Xk = (zk)./(zk-0.7);
xn = real(invdfs(Xk,N));
xtilde = xn'* ones(1,4); xtilde = (xtilde(:))';
subplot(2,2,2); stem(0:39,xtilde,"-");
xtitle("n"); ytitle("xtilde(n)"); title("N=10")//
N = 20;
k = 0:N-1:1;
wk = 2*pi*k/N;
zk = exp(j*wk);
Xk = (zk)./(zk-0.7);
xn = real(invdfs(Xk,N));
xtilde = xn'* ones(1,2); xtilde = (xtilde(:))';
subplot(2,2,3); stem(0:39,xtilde,"-");
xtitle("n"); ytitle("xtilde(n)"); title("N=20")//
N = 40;
k = 0:N-1:1;
wk = 2*pi*k/N;
zk = exp(j*wk);
Xk = (zk)./(zk-0.7);
xn = real(invdfs(Xk,N));
subplot(2,2,4); stem(0:39,xn,"-");
xtitle("n"); ytitle("xtilde(n)"); title("N=40")