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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 8.11 \n\n');

banner();

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

%d = 0.10

%d = 0.05

d = 0.01

a1 = (2-d)/(1+d);

a2 = (2-d)*(1-d)/((2+d)*(1+d));

% digital IIR 2nd-order allpass filter

b = [a2  a1  1]

a = [1  a1  a2]

figure('NumberTitle', 'off', 'Name', 'Problem 8.11 Pole-Zero Plot')

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

zplane(b,a);

title(sprintf('Pole-Zero Plot, d=%.2f',d));

%pzplotz(b,a);

[db, mag, pha, grd, w] = freqz_m(b, a);

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

%  Choose the gain parameter of the filter, maximum gain is equal to 1

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

gain1=max(mag)                    % with poles

K = 1

[db, mag, pha, grd, w] = freqz_m(K*b, a);

figure('NumberTitle', 'off', 'Name', 'Problem 8.11 IIR allpass filter')

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

subplot(2,2,1); plot(w/pi, db); grid on; axis([0 2 -60 10]);

set(gca,'YTickMode','manual','YTick',[-60,-30,0])

set(gca,'YTickLabelMode','manual','YTickLabel',['60';'30';' 0']);

set(gca,'XTickMode','manual','XTick',[0,0.25,0.5,1,1.5,1.75,2]);

xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude Response in dB');

subplot(2,2,3); plot(w/pi, mag); grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Absolute'); title('Magnitude Response in absolute');

set(gca,'XTickMode','manual','XTick',[0,0.25,0.5,1,1.5,1.75,2]);

set(gca,'YTickMode','manual','YTick',[0,1.0]);

subplot(2,2,2); plot(w/pi, pha); grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Rad'); title('Phase Response in Radians');

subplot(2,2,4); plot(w/pi, grd*pi/180);  grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Rad'); title('Group Delay');

set(gca,'XTickMode','manual','XTick',[0,0.25,0.5,1,1.5,1.75,2]);

%set(gca,'YTickMode','manual','YTick',[0,1.0]);

figure('NumberTitle', 'off', 'Name', 'Problem 8.11 IIR allpass filter')

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

plot(w/pi, -pha/w); grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Rad'); title('Phase Delay in samples');

% Impulse Response

fprintf('\n----------------------------------');

fprintf('\nPartial fraction expansion method: \n');

[R, p, c] = residuez(K*b,a)

MR = (abs(R))'              % Residue  Magnitude

AR = (angle(R))'/pi         % Residue  angles in pi units

Mp = (abs(p))'              % pole  Magnitude

Ap = (angle(p))'/pi         % pole  angles in pi units

[delta, n] = impseq(0,0,20);

h_chk = filter(K*b,a,delta);      % check sequences

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

%                                gain parameter K

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

%h =  0.2202 * ((-0.9385) .^ n) + (-0.8308) * ((-0.7887) .^ n) + 1.3509 * delta;    %d=0.1

%h =  0.1099 * ((-0.9688) .^ n) + (-0.4112) * ((-0.8884) .^ n) + 1.1619 * delta;    %d=0.05

h =  0.0220 * ((-0.9937) .^ n) + (-0.0820) * ((-0.9766) .^ n) + 1.0305 * delta;    %d=0.01

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

figure('NumberTitle', 'off', 'Name', 'Problem 8.11 IIR allpass filter, h(n) by filter and Inv-Z ')

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

subplot(2,1,1); stem(n, h_chk); grid on; %axis([0 2 -60 10]);

xlabel('n'); ylabel('h\_chk'); title('Impulse Response sequences by filter');

subplot(2,1,2); stem(n, h); grid on; %axis([0 1 -100 10]);

xlabel('n'); ylabel('h'); title('Impulse Response sequences by Inv-Z');

[db, mag, pha, grd, w] = freqz_m(h, [1]);

figure('NumberTitle', 'off', 'Name', 'Problem 8.11 IIR filter, h(n) by Inv-Z ')

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

subplot(2,2,1); plot(w/pi, db); grid on; axis([0 2 -60 10]);

set(gca,'YTickMode','manual','YTick',[-60,-30,0])

set(gca,'YTickLabelMode','manual','YTickLabel',['60';'30';' 0']);

set(gca,'XTickMode','manual','XTick',[0,0.25,1,1.75,2]);

xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude Response in dB');

subplot(2,2,3); plot(w/pi, mag); grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Absolute'); title('Magnitude Response in absolute');

set(gca,'XTickMode','manual','XTick',[0,0.25,1,1.75,2]);

set(gca,'YTickMode','manual','YTick',[0,1.0]);

subplot(2,2,2); plot(w/pi, pha); grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Rad'); title('Phase Response in Radians');

subplot(2,2,4); plot(w/pi, grd*pi/180);  grid on; %axis([0 1 -100 10]);

xlabel('frequency in \pi units'); ylabel('Rad'); title('Group Delay');

set(gca,'XTickMode','manual','XTick',[0,0.25,1,1.75,2]);

%set(gca,'YTickMode','manual','YTick',[0,1.0]);