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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 4.18 \n\n');

banner();

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

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

%       1   H1(z)

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

b = 1/4*[1, 2, 0, 1]; a = [1];               %  

[R, p, C] = residuez(b,a)

Mp = (abs(p))'

Ap = (angle(p))'/pi

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

%%   START a    determine H(z) and sketch

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

figure('NumberTitle', 'off', 'Name', 'P4.18.1 H(z) its pole-zero plot')

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

zplane(b,a);

title('pole-zero plot'); grid on;

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

%%    END

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

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

%               y1(n)  Output

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

yb1 = conv(b, [2]);

ya1 = conv(a, [1,-0.9]);

[R1, p1, C1] = residuez(yb1, ya1)

Mp = (abs(p1))'

Ap = (angle(p1))'/pi

[delta, n] = impseq(0, 0, 7);

y1_check = filter(yb1, ya1, delta)                                             % check sequence

y1_answer = -1.7970*impseq(0,0,7) - 0.6173*impseq(1,0,7) - 0.5556*impseq(2,0,7) + 2.2970*(0.9).^n .* stepseq(0,0,7)         % answer sequence