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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 8.32 \n\n');

banner();

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

%           Ω=(2/T)tan(ω/2)

%           ω=2*[atan(ΩT/2)]

%     Digital Filter Specifications:

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

wp = 0.3*pi;                     % digital passband freq in rad

ws = 0.4*pi;                     % digital stopband freq in rad

Rp = 0.25;                       % passband ripple in dB

As = 50;                         % stopband attenuation in dB

Ripple = 10 ^ (-Rp/20)           % passband ripple in absolute

Attn = 10 ^ (-As/20)             % stopband attenuation in absolute

% Analog prototype specifications: Inverse Mapping for frequencies

T = 1;                           % set T = 1

Fs = 1/T;

OmegaP = (2/T)*tan(wp/2)        % prototype passband freq

OmegaS = (2/T)*tan(ws/2)        % prototype stopband freq      

% Analog Elliptic Prototype Filter Calculation:

[cs, ds] = afd_elip(OmegaP, OmegaS, Rp, As);

% Calculation of second-order sections:

fprintf('\n***** Cascade-form in s-plane: START *****\n');

[CS, BS, AS] = sdir2cas(cs, ds)

fprintf('\n***** Cascade-form in s-plane: END *****\n');

% Calculation of Frequency Response:

[db_s, mag_s, pha_s, ww_s] = freqs_m(cs, ds, 0.5*pi/T);

% Calculation of Impulse Response:

[ha, x, t] = impulse(cs, ds);

% Impulse Invariance Transformation:

%[b, a] = imp_invr(cs, ds, T); 

% Bilinear Transformation

[b, a] = bilinear(cs, ds, Fs)

[C, B, A] = dir2cas(b, a)

% Calculation of Frequency Response:

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

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

%%                             Plot

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figure('NumberTitle', 'off', 'Name', 'Problem 8.32 Analog Elliptic lowpass')

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

M = 1.0;                          % Omega max

subplot(2,2,1); plot(ww_s/pi, mag_s);  grid on; %axis([-10, 10, 0, 1.2]);

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

set(gca, 'XTickMode', 'manual', 'XTick', [-0.4625, -0.3244, 0, 0.3244, 0.4625]);

set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.0032, 0.9716, 1.0, 1.5]);

subplot(2,2,2); plot(ww_s/pi, db_s);  grid on; %axis([0, M, -50, 10]);

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

set(gca, 'XTickMode', 'manual', 'XTick', [-0.4625, -0.3244, 0, 0.3244, 0.417, 0.458, 0.4625]);

set(gca, 'YTickMode', 'manual', 'YTick', [-50, -1, 0]);

set(gca,'YTickLabelMode','manual','YTickLabel',['50';' 1';' 0']);

subplot(2,2,3); plot(ww_s/pi, pha_s/pi);  grid on; %axis([-10, 10, -1.2, 1.2]);

xlabel('Analog frequency in \pi nuits'); ylabel('radians'); title('Phase Response');

set(gca, 'XTickMode', 'manual', 'XTick', [-0.4625, -0.3244, 0, 0.3244, 0.4625]);

set(gca, 'YTickMode', 'manual', 'YTick', [-1:0.5:1]);

subplot(2,2,4); plot(t, ha); grid on; %axis([0, 30, -0.05, 0.25]);

xlabel('time in seconds'); ylabel('ha(t)'); title('Impulse Response');

figure('NumberTitle', 'off', 'Name', 'Problem 8.32 Digital Elliptic lowpass by bilinear')

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

M = 2;                          % Omega max

subplot(2,2,1); plot(ww/pi, mag); axis([0, M, 0, 1.2]); grid on;

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.3, 0.4, 1.6, 1.7, M]);

set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.0032, 0.9716, 1]);

subplot(2,2,2); plot(ww/pi, pha/pi); axis([0, M, -1.1, 1.1]); grid on;

xlabel('Digital frequency in \pi nuits'); ylabel('radians in \pi units'); title('Phase Response');

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.3, 0.4, 1.6, 1.7, M]);

set(gca, 'YTickMode', 'manual', 'YTick', [-1:1:1]);

subplot(2,2,3); plot(ww/pi, db); axis([0, M, -80, 10]); grid on;

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.3, 0.37, 0.4, 1.6, 1.7, M]);

set(gca, 'YTickMode', 'manual', 'YTick', [-60, -50, -1, 0]);

set(gca,'YTickLabelMode','manual','YTickLabel',['60';'50';' 1';' 0']);

subplot(2,2,4); plot(ww/pi, grd); grid on; %axis([0, M, 0, 35]);

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.3, 0.4, 1.6, 1.7, M]);

%set(gca, 'YTickMode', 'manual', 'YTick', [0:5:35]);

figure('NumberTitle', 'off', 'Name', 'Problem 8.32 Pole-Zero Plot')

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

zplane(b,a);

title(sprintf('Pole-Zero Plot'));

%pzplotz(b,a);

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

%       Calculation of Impulse Response

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

figure('NumberTitle', 'off', 'Name', 'Problem 8.32 Imp & Freq Response')

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

t = [0:0.01:90]; subplot(2,1,1); impulse(cs,ds,t); grid on;   % Impulse response of the analog filter

axis([0,90,-0.2,0.3]);hold on

n = [0:1:90/T]; hn = filter(b,a,impseq(0,0,90/T));           % Impulse response of the digital filter

stem(n*T,hn); xlabel('time in sec'); title (sprintf('Impulse Responses T=%2d',T));

hold off

% Calculation of Frequency Response:

[dbs, mags, phas, wws] = freqs_m(cs, ds, 2*pi/T);             % Analog frequency   s-domain  

[dbz, magz, phaz, grdz, wwz] = freqz_m(b, a);                  % Digital  z-domain

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

%%                             Plot

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

subplot(2,1,2); plot(wws/(2*pi), mags/T,'b', wwz/(2*pi*T), magz, 'r'); grid on;

xlabel('frequency in Hz'); title('Magnitude Responses'); ylabel('Magnitude'); 

text(-0.8,0.15,'Analog filter', 'Color', 'b'); text(0.8,0.4,'Digital filter', 'Color', 'r');