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fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 5.29 \n\n');

banner();

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

%       x1(n) and x2(n) ----  N-point sequence

%        y(n) = x1(n) Cir-Conv x2(n)

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

N = 8;

n1 = [0:N-1];

x1 = [9, 4, -1, 4, -4, -1, 8, 3];

N1 = length(x1);

n2 = [0:N-1];

x2 = [-5, 6, 2, -7, -5, 2, 2, -2];

N2 = length(x2);

sum_x1 = sum( x1( min(n1)+1 : max(n1)+1 ) )

sum_x2 = sum( x2( min(n2)+1 : max(n2)+1 ) )

answer = sum_x1 * sum_x2

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

%        1st way TIME domain

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

%N = 10;

n = [0:N-1];

y1 = circonvt(x1, x2, N);

sum_y1 = sum( y1( min(n)+1 : max(n)+1 ) )

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

%   2nd way ----  circular conv(FREQ domain)

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

y2 = circonvf(x1, x2, N);

sum_y2 = sum( y2( min(n)+1 : max(n)+1 ) )

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

%   3rd way --- Cir Conv (Circulant Matrix)

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

y3 = circonvt_v3(x1, x2, N);

sum_y3 = sum( y3( min(n)+1 : max(n)+1 ) )

figure('NumberTitle', 'off', 'Name', 'P5.29 x1(n) and x2(n)')

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

subplot(2,1,1); stem(n1, x1);

xlabel('n'); ylabel('x1(n)');

title('x1(n)  N=8');  grid on;

subplot(2,1,2); stem(n2, x2);

%axis([-N/2, N/2, -0.5, 50.5]);

xlabel('n'); ylabel('x2(n)');

title('x2(n)  N=8');  grid on;

figure('NumberTitle', 'off', 'Name', 'P5.29 Cir-Conv, N=8')

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

subplot(3,1,1); stem(n, y1);

xlabel('n'); ylabel('y1(n)');

title('Time Domain, y1(n)');  grid on;

subplot(3,1,2); stem(n, y2);

%axis([0, N, 0, 1]);

xlabel('n'); ylabel('y2(n)');

title('FREQ domain, y2(n)');  grid on;

subplot(3,1,3); stem(n, y3);

%axis([-N/2, N/2, -0.5, 50.5]);

xlabel('n'); ylabel('y3(n)');

title('Circulant Matrix, y3(n)');  grid on;