《DSP using MATLAB》Problem 8.37

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 8.37 \n\n');

banner();
%% ------------------------------------------------------------------------

% Digital Filter Specifications:   Chebyshev-2 bandpass
ws = [0.30*pi 0.60*pi];             % digital stopband freq in rad
wp = [0.40*pi 0.50*pi];             % digital passband freq in rad
Rp = 0.50;                          % 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

% Calculation of Chebyshev-2 filter parameters:
[N, wn] = cheb2ord(wp/pi, ws/pi, Rp, As);

fprintf('\n  ********* Chebyshev-2 Digital Bandpass Filter Order is = %3.0f \n', 2*N)

% Digital Chebyshev-2 Bandpass Filter Design:
[bbp, abp] = cheby2(N, As, wn);

[C, B, A] = dir2cas(bbp, abp)

% Calculation of Frequency Response:
%[dblp, maglp, phalp, grdlp, wwlp] = freqz_m(blp, alp);
[dbbp, magbp, phabp, grdbp, wwbp] = freqz_m(bbp, abp);

% ---------------------------------------------------------------
%    find Actual Passband Ripple and Min Stopband attenuation
% ---------------------------------------------------------------
delta_w = 2*pi/1000;
Rp_bp = -(min(dbbp(ceil(wp(1)/delta_w+1):1:ceil(wp(2)/delta_w+1))));      % Actual Passband Ripple

fprintf('\nActual Passband Ripple is %.4f dB.\n', Rp_bp);

As_bp = -round(max(dbbp(1:1:ceil(ws(1)/delta_w)+1)));                    % Min Stopband attenuation
fprintf('\nMin Stopband attenuation is %.4f dB.\n\n', As_bp);

%% -----------------------------------------------------------------
%%                             Plot
%% -----------------------------------------------------------------  

figure('NumberTitle', 'off', 'Name', 'Problem 8.37 Chebyshev-2 bp by cheby2 function')
set(gcf,'Color','white');
M = 1;                          % Omega max

subplot(2,2,1); plot(wwbp/pi, magbp); 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, 0.5, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.9441, 1]);

subplot(2,2,2); plot(wwbp/pi, dbbp); axis([0, M, -100, 2]); grid on;
xlabel('Digital frequency in \pi units'); ylabel('Decibels'); title('Magnitude in dB');
set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.3, 0.4, 0.5, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [-80, -50, -1, 0]);
set(gca,'YTickLabelMode','manual','YTickLabel',['80'; '50';'1 ';' 0']);

subplot(2,2,3); plot(wwbp/pi, phabp/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, 0.5, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [-1:0.5:1]);

subplot(2,2,4); plot(wwbp/pi, grdbp); axis([0, M, 0, 40]); grid on;
xlabel('Digital frequency in \pi units'); ylabel('Samples'); title('Group Delay');
set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.3, 0.4, 0.5, 0.6, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [0:10:40]);

　　运行结果：

通带、阻带绝对指标

用cheby2函数（MATLAB自带），设计数字低通原型滤波器，阶数为5，系统函数串联形式的系数为

Chebyshev-2型数字低通，幅度谱、相位谱和群延迟响应