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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 2.19 \n\n');

banner();

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

b = [1, 2, 0, 1]; a = [1, -0.5, 0.25];

n = [0:100];

h1 = impz(b, a, n);

x = impseq(0, 0, 100);

h2 = filter(b, a, x);

figure('NumberTitle', 'off', 'Name', 'Problem 2.19 Impulse response')

set(gcf,'Color',[1,1,1])                  % 改变坐标外围背景颜色

subplot(2,1,1); stem(n, h1); title('impz function');

xlabel('n'); ylabel('h1(n)') ;

grid on

subplot(2,1,2); stem(n, h2); title('filter function');

xlabel('n'); ylabel('h2(n)');

grid on;

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

%%       stability

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

fprintf('\n1st impz  :  sum(abs(h)) = %f \n', sum(abs(h1)));

fprintf('\n2nd filter:  sum(abs(h)) = %f \n', sum(abs(h2)));

figure('NumberTitle', 'off', 'Name', 'Problem 2.19 Zero-Pole')

set(gcf,'Color',[1,1,1])                  % 改变坐标外围背景颜色

pzmap(b, a);

z = roots(a); magz = abs(z)

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

%%           another input

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

n2 = [0:200];

x2 = (5 + 3*cos(0.2*pi*n2) + 4*sin(0.6*pi*n2)) .* stepseq(0, 0, 200);

y2 = filter(b, a, x2);

figure('NumberTitle', 'off', 'Name', 'Problem 2.19 Another input')

set(gcf,'Color',[1,1,1])                  % 改变坐标外围背景颜色

subplot(2,1,1); stem(n2, x2); title('input');

xlabel('n2'); ylabel('x2(n)') ;

grid on

subplot(2,1,2); stem(n2, y2); title('Output');

xlabel('n2'); ylabel('y2(n)');

grid on;