신호  일 때, evenodd 함수를 이용하여 의 우함수부와 기함수부를 계산하고, 각 부분의 이산 시간 푸리에 변환을 구해보자.

ex3_12.cem

 n = -5:10; x = sin(pi*n/2);
 k = -100:100; w = (pi/100)*k;             /* frequency between -pi and +pi */
 X = x * (exp(-j*pi/100)).^(n'*k);         /* DTFT of x */
 /* signal decomposition */
 [xe,xo,m] = oddeven(x,n);                 /* even and odd parts */
 XE = xe * (exp(-j*pi/100)).^(m'*k);       /* DTFT of xe */
 XO = xo * (exp(-j*pi/100)).^(m'*k);       /* DTFT of xo */
 /* verification */
 XR = real(X);                             /* real part of X */
error1 = max(abs(XE-XR))                        /* Difference */
error1 =
  1.8974e-019
 XI = imag(X);                             /* imag part of X */
 error2 = max(abs(XO-j*XI))                /* Difference */
error2 =
  1.8033e-019
 /* graphical verification */
 subplot(1,1,1);
 subplot(2,2,1); plot(w/pi,XR);
 xtitle("frequency in pi units"); ytitle("Re(X)");
 title("Real part of X");
 subplot(2,2,2); plot(w/pi,XI);
 xtitle("frequency in pi units"); ytitle("Im(X)");
 title("Imaginary part of X");
 subplot(2,2,3); plot(w/pi,real(XE));
 xtitle("frequency in pi units"); ytitle("XE");
 title("Transform of even part");
 subplot(2,2,4); plot(w/pi,imag(XO));
 xtitle("frequency in pi units"); ytitle("XO");
 title("Transform of odd part");