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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Exameple 8.22 \n\n');

time_stamp = datestr(now, 31);

[wkd1, wkd2] = weekday(today, 'long');

fprintf('      Now is %20s, and it is %8s  \n\n', time_stamp, wkd2);

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

% Digital Filter Specifications:

wp = 0.2*pi;                 % digital passband freq in rad

ws = 0.3*pi;                 % digital stopband freq in rad

Rp = 1;                      % passband ripple in dB

As = 15;                     % stopband attenuation in dB

% Analog prototype specifications: Inverse Mapping for frequencies

T = 1;                           % set T = 1

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

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

% Analog Prototype Order Calculations:

ep = sqrt(10^(Rp/10)-1);           % Passband Ripple Factor

A = 10^(As/20);                    % Stopband Attenuation Factor

OmegaC = OmegaP;                   % Analog Chebyshev-1 prototype cutoff freq

OmegaR = OmegaS/OmegaP;            % Analog prototype Transition ratio

g = sqrt(A*A-1)/ep;                % Analog prototype Intermediate cal

N  = ceil(log10(g+sqrt(g*g-1))/log10(OmegaR+sqrt(OmegaR*OmegaR-1)));

fprintf('\n\n ********** Chebyshev-I Filter Order = %3.0f  \n', N)

% Digital Chebyshev-1 Filter Design:

wn = wp/pi;                        % Digital Chebyshev-1 cutoff freq in pi units

[b, a] = cheby1(N, Rp, wn); [C, B, A] = dir2cas(b, a)

% Calculation of Frequency Response:

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

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

%%                             Plot

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

figure('NumberTitle', 'off', 'Name', 'Exameple 8.22')

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

M = 1;                          % Omega max

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

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]);

set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.1778, 0.8913, 1]);

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

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]);

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

subplot(2,2,3); plot(ww/pi, db); axis([0, M, -30, 10]); grid on;

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]);

set(gca, 'YTickMode', 'manual', 'YTick', [-30, -15, -1, 0]);

subplot(2,2,4); plot(ww/pi, grd); axis([0, M, 0, 15]); grid on;

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

set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.2, 0.3, M]);

set(gca, 'YTickMode', 'manual', 'YTick', [0:5:15]);