b = [0.0181,  0.0543, 0.0543,  0.0181];         % filter coefficient array b

a = [1.0000, -1.7600, 1.1829, -0.2781];         % filter coefficient array a

m = 0:length(b)-1; l = 0:length(a)-1;           % index arrays m and l

K = 500; k = 0:1:K;                             % index array k for frequencies

w = k*pi/500;                                   % freqency between 0 and +pi, [0,pi] axis divided into 501 points.

num = b * exp(-j*m'*w);                         % Numerator calculations

den = a * exp(-j*l'*w);                         % Denominator claculations

H = num ./ den;                                 % Frequency response

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

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

%%              START H's  mag ang real imag

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

figure('NumberTitle', 'off', 'Name', 'Example3.16');

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 X's  mag ang real imag

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