n = 0:10; x = 10*(0.8) .^ n;

[xec, xoc] = circevod(x);

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%%                  START   a

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figure('NumberTitle', 'off', 'Name', 'Exameple5.10a x sequence')

set(gcf,'Color','white');

subplot(3,1,1); stem(n,x); title('Original sequence x(n)'); %axis([0,10,-2.5,2.5]);

xlabel('n'); ylabel('x(n)'); grid on;

subplot(3,1,2); stem(n,xec); title('Circular-even component'); axis([-0.5,10.5,-1,11]);

xlabel('n'); ylabel('xec(n)'); grid on;

subplot(3,1,3); stem(n,xoc); title('Circular-odd component'); axis([-0.5,10.5,-4,4]);

xlabel('n'); ylabel('xoc(n)'); grid on;

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%%                  END   a

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%%              START   b

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X_DFT = dft(x,11);                                       % DFT of x

Xec_DFT = dft(xec,11); Xoc_DFT = dft(xoc,11);            % DFT of xec and xoc

realX_DFT = real(X_DFT); imagX_DFT = imag(X_DFT); magX_DFT = abs(X_DFT(1:1:6)); phaX_DFT = angle(X_DFT(1:1:6))*180/pi;

realXec_DFT = real(Xec_DFT); imagXec_DFT = imag(Xec_DFT); magXec_DFT = abs(Xec_DFT(1:1:6)); phaXec_DFT = angle(Xec_DFT)*180/pi;

realXoc_DFT = real(Xoc_DFT); imagXoc_DFT = imag(Xoc_DFT); magXoc_DFT = abs(Xoc_DFT(1:1:6)); phaXoc_DFT = angle(Xoc_DFT)*180/pi;

figure('NumberTitle', 'off', 'Name', 'Exameple5.10b ')

set(gcf,'Color','white');

subplot(2,2,1); stem(n,realX_DFT); title('Real {DFT[x(n)]}'); axis([-0.5,10.5,-5,50]);

xlabel('k'); grid on;

subplot(2,2,2); stem(n,imagX_DFT); title('Imag {DFT[x(n)]}'); axis([-0.5,10.5,-20,20]);

xlabel('k'); grid on;

subplot(2,2,3); stem(n,realXec_DFT); title('Real {DFT[xec(n)]}'); axis([-0.5,10.5,-5,50]);

xlabel('k'); grid on;

subplot(2,2,4); stem(n,imagXoc_DFT); title('Imag {DFT[xoc(n)]}'); axis([-0.5,10.5,-20,20]);

xlabel('k'); grid on;

figure('NumberTitle', 'off', 'Name', 'Exameple5.10b X DFT info')

set(gcf,'Color','white');

subplot(2,2,1); stem(n,realX_DFT); title('Real {DFT[x(n)]}'); axis([-0.5,10.5,-5,50]);

xlabel('k'); grid on;

subplot(2,2,2); stem(n,imagX_DFT); title('Imag {DFT[x(n)]}'); axis([-0.5,10.5,-20,20]);

xlabel('k'); grid on;

k = 0:1:5; w = 2*pi/10*k;

subplot(2,2,3); stem(w/pi,magX_DFT); title('Magnitude DTFT'); %axis([-0.5,10.5,-5,50]);

xlabel('frequency in \pi units'); grid on;

subplot(2,2,4); stem(w/pi,phaX_DFT); title('Angle {DFT[x(n)]}'); %axis([-0.5,10.5,-20,20]);

xlabel('frequency in \pi units'); grid on;

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%%                    END   b

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