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Highlights from
Digital Signal Processing Using MATLAB

Digital Signal Processing Using MATLAB

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21 Aug 2002 (Updated )

Companion Software

ex031200.m
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')

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