%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 5.31 \n\n');

banner();

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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

%   x3(n) --- N-point circular convolution of x1(n) an x2(n)

%   x4(n) ---          Linear convolution

%   e(n)  ---       error sequence

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

N = 15;

n1 = [0:9];

x1 = 0.8.^n1;

N1 = length(x1);

n2 = [0:9];

x2 = (-0.8).^n2;

N2 = length(x2);

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

%        1st way ---- time domain

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

y1 = circonvt(x1, x2, N)

ny1 = [0:N-1];

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

%   2nd way ----  DFT method

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

y2 = circonvf(x1, x2, N);

ny2 = [0:N-1];

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

%   3rd way --- circulant matrix

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

y3 = circonvt_v3(x1, x2, N);

ny3 = [0:N-1];

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

%     Linear convolution

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

[y4, ny4] = conv_m(x1, n1, x2, n2);

e1 = y1 - y4(1:N);

figure('NumberTitle', 'off', 'Name', 'P5.31.3 x1(n) and x2(n)')

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

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

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

title('x1(n)=0.8^n  N=10');  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)=(-0.8)^n  N=10');  grid on;

figure('NumberTitle', 'off', 'Name', 'P5.31.3 Cir-Conv and Linear-Conv')

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

subplot(2,2,1); stem(ny1, y1);

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

title('Cir-Conv (Time domain), y1(n)');  grid on;

subplot(2,2,2); stem(ny2, y2);

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

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

title('Cir-Conv (DFT method), y2(n)');  grid on;

subplot(2,2,3); stem(ny3, y3);

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

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

title('Cir-Conv (circulant matrix), y3(n)');  grid on;

subplot(2,2,4); stem(ny4, y4);

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

xlabel('n'); ylabel('y4(n)');

title('Linear-Conv, y4(n)');  grid on;