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] = evenodd(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
XI = imag(X);                        % imag part of X
error2 = max(abs(XO-j*XI))           % Difference
% graphical verification
subplot(1,1,1)
subplot(2,2,1); plot(w/pi,XR); grid; axis([-1,1,-2,2])
xlabel('frequency in pi units'); ylabel('Re(X)');
title('Real part of X')
subplot(2,2,2); plot(w/pi,XI); grid; axis([-1,1,-10,10])
xlabel('frequency in pi units'); ylabel('Im(X)');
title('Imaginary part of X')
subplot(2,2,3); plot(w/pi,real(XE)); grid; axis([-1,1,-2,2])
xlabel('frequency in pi units'); ylabel('XE');
title('Transform of even part')
subplot(2,2,4); plot(w/pi,imag(XO)); grid; axis([-1,1,-10,10])
xlabel('frequency in pi units'); ylabel('XO');
title('Transform of odd part')