n = 0:10; x = 10*(0.8) .^ n; y = x(mod_1(-n,11)+1);

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%%                  START   a

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figure('NumberTitle', 'off', 'Name', 'Exameple5.9a x sequence')

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

subplot(2,1,1); stem(n,x); title('Original sequence x(n)'); %axis([0,10,-2.5,2.5]);

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

subplot(2,1,2); stem(n,y); title('Circularly folded sequence y(n)'); %axis([0,10,-2.5,2.5]);

xlabel('n'); ylabel('y(n)=x(-n mod 10)'); grid on;

%% -----------------------------------------------------------------

%%                  END   a

%% -----------------------------------------------------------------

%% -----------------------------------------------------------------

%%              START   b

%% -----------------------------------------------------------------

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

realX_DFT = real(X_DFT); imagX_DFT = imag(X_DFT);

realY_DFT = real(Y_DFT); imagY_DFT = imag(Y_DFT);

figure('NumberTitle', 'off', 'Name', 'Exameple5.9b x sequence')

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

subplot(2,2,1); stem(n,realX_DFT); title('Real {DFT[x(n)]}'); %axis([0,N,-0.5,1.5]);

xlabel('k'); grid on;

subplot(2,2,2); stem(n,imagX_DFT); title('Imag {DFT[x(n)]}'); %axis([0,N,-0.5,1.5]);

xlabel('k'); grid on;

subplot(2,2,3); stem(n,realY_DFT); title('Real {DFT[x((-n))11]}'); %axis([0,N,-0.5,1.5]);

xlabel('k'); grid on;

subplot(2,2,4); stem(n,imagY_DFT); title('Imag {DFT[x((-n))11]}'); %axis([0,N,-0.5,1.5]);

xlabel('k'); grid on;

%% -----------------------------------------------------------------

%%                    END   b

%% -----------------------------------------------------------------