《DSP using MATLAB》示例Example 8.21

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf(‘\n***********************************************************\n‘);
fprintf(‘        <DSP using MATLAB> Exameple 8.21 \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:
N  = ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(OmegaP/OmegaS)));
fprintf(‘\n\n ********** Butterworth Filter Order = %3.0f  \n‘, N)

OmegaC = OmegaP/((10^(Rp/10)-1)^(1/(2*N)));       % Analog BW prototype cutoff freq
wn = 2*atan((OmegaC*T)/2);                        % Digital BW cutoff freq

% Digital Butterworth Filter Design:
wn = wn/pi;                            % Digital Butterworth cutoff freq in pi units

[b, a] = butter(N, 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 8.21‘)
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]);