b = [1, 0]; a = [1, -0.9];               %  

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

%%   START a    determine H(z) and sketch

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

figure('NumberTitle', 'off', 'Name', 'Example4.11a H(z) its pole-zero plot')

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

zplane(b,a);

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

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

%%    END

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

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

%%    START    b   |H|   <H

%%    1st form of freqz

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

[H,w] = freqz(b,a,100);                 % 1st form of freqz

magH  = abs(H);  angH  = angle(H);  realH  = real(H);  imagH  = imag(H);

%% ================================================

%%              START H's  mag ang real imag

%% ================================================

figure('NumberTitle', 'off', 'Name', 'Example4.11b H its mag ang real imag');

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

subplot(2,2,1); plot(w/pi,magH); grid on;  %axis([0,1,0,1.5]);

title('Magnitude Response');

xlabel('frequency in \pi units'); ylabel('Magnitude  |H|');

subplot(2,2,3); plot(w/pi, angH/pi); grid on; % axis([-1,1,-1,1]);

title('Phase Response');

xlabel('frequency in \pi units'); ylabel('Radians/\pi');

subplot('2,2,2'); plot(w/pi, realH); grid on;

title('Real Part');

xlabel('frequency in \pi units'); ylabel('Real');

subplot('2,2,4'); plot(w/pi, imagH); grid on;

title('Imaginary Part');

xlabel('frequency in \pi units'); ylabel('Imaginary');

%% ==================================================

%%             END H's  mag ang real imag

%% ==================================================

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

%%    END    b   |H|   <H

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

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

%%    START    b   |H|   <H

%%    2nd form of freqz

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

[H,w] = freqz(b,a,200,'whole');                 % 2nd form of freqz

magH  = abs(H(1:101));  angH  = angle(H(1:101));  realH  = real(H);  imagH  = imag(H);

%% ================================================

%%              START H's  mag ang real imag

%% ================================================

figure('NumberTitle', 'off', 'Name', 'Example4.11b  using 2nd form freqz ');

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

subplot(2,2,1); plot(w/pi,magH); grid on;  %axis([0,1,0,1.5]);

title('Magnitude Response');

xlabel('frequency in \pi units'); ylabel('Magnitude  |H|');

subplot(2,2,3); plot(w/pi, angH/pi); grid on; % axis([-1,1,-1,1]);

title('Phase Response');

xlabel('frequency in \pi units'); ylabel('Radians/\pi');

subplot('2,2,2'); plot(w/pi, realH); grid on;

title('Real Part');

xlabel('frequency in \pi units'); ylabel('Real');

subplot('2,2,4'); plot(w/pi, imagH); grid on;

title('Imaginary Part');

xlabel('frequency in \pi units'); ylabel('Imaginary');

%% ==================================================

%%             END H's  mag ang real imag

%% ==================================================

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

%%    END    b   |H|   <H

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

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

%%    START    b   |H|   <H

%%    3rd form of freqz

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

w = [0:1:100]*pi/100;     H = freqz(b,a,w);

%[H,w] = freqz(b,a,200,'whole');                 % 3rd form of freqz

magH  = abs(H);  angH  = angle(H);  realH  = real(H);  imagH  = imag(H);

%% ================================================

%%              START H's  mag ang real imag

%% ================================================

figure('NumberTitle', 'off', 'Name', 'Example4.11b  using 3rd form freqz ');

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

subplot(2,2,1); plot(w/pi,magH); grid on;  %axis([0,1,0,1.5]);

title('Magnitude Response');

xlabel('frequency in \pi units'); ylabel('Magnitude  |H|');

subplot(2,2,3); plot(w/pi, angH/pi); grid on; % axis([-1,1,-1,1]);

title('Phase Response');

xlabel('frequency in \pi units'); ylabel('Radians/\pi');

subplot('2,2,2'); plot(w/pi, realH); grid on;

title('Real Part');

xlabel('frequency in \pi units'); ylabel('Real');

subplot('2,2,4'); plot(w/pi, imagH); grid on;

title('Imaginary Part');

xlabel('frequency in \pi units'); ylabel('Imaginary');

%% ==================================================

%%             END H's  mag ang real imag

%% ==================================================

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

%%    END    b   |H|   <H

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