《DSP using MATLAB》Problem 8.21

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 8.21 \n\n');
 
banner();
%% ------------------------------------------------------------------------
 
Fp = 3.2;                    % analog passband freq in kHz
Fs = 3.8;                    % analog stopband freq in kHz
fs = 8;                      % sampling rate in kHz
 
% -------------------------------
%       ω = ΩT = 2πF/fs
% Digital Filter Specifications:
% -------------------------------
%wp = 2*pi*Fp/fs;                 % digital passband freq in rad/sec
wp = Fp;
%ws = 2*pi*Fs/fs;                 % digital stopband freq in rad/sec
ws = Fs;
Rp = 0.5;                        % passband ripple in dB
As = 45;                         % 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
OmegaP = wp/T;               % prototype passband freq
OmegaS = ws/T;               % prototype stopband freq
 
% Analog Chebyshev-1 Prototype Filter Calculation:
[cs, ds] = afd_chb1(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, 8);
 
% Calculation of Impulse Response:
[ha, x, t] = impulse(cs, ds);
 
% Impulse Invariance Transformation:
[b, a] = imp_invr(cs, ds, T); [C, B, A] = dir2par(b, a)
 
% Calculation of Frequency Response:
[db, mag, pha, grd, ww] = freqz_m(b, a);
 
%% -----------------------------------------------------------------
%%                             Plot
%% -----------------------------------------------------------------
figure('NumberTitle', 'off', 'Name', 'Problem 8.21 Analog Chebyshev-I lowpass')
set(gcf,'Color','white');
M = 1.0;                          % Omega max
 
subplot(2,2,1); plot(ww_s, mag_s/T);  grid on; %axis([-10, 10, 0, 1.2]);
xlabel(' Analog frequency in kHz units'); ylabel('|H|'); title('Magnitude in Absolute');
set(gca, 'XTickMode', 'manual', 'XTick', [-8, -3.8, -3.2, 0, 3.2, 3.8, 8]);
set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.006, 0.94, 1]);
 
subplot(2,2,2); plot(ww_s, db_s);  grid on; %axis([0, M, -50, 10]);
xlabel('Analog frequency in kHz units'); ylabel('Decibels'); title('Magnitude in dB ');
set(gca, 'XTickMode', 'manual', 'XTick', [-8, -3.8, 0, 3.2, 3.8, 8]);
set(gca, 'YTickMode', 'manual', 'YTick', [-45, -1, 0]);
set(gca,'YTickLabelMode','manual','YTickLabel',['45';' 1';' 0']);
 
subplot(2,2,3); plot(ww_s, pha_s/pi);  grid on; axis([-10, 10, -1.2, 1.2]);
xlabel('Analog frequency in kHz nuits'); ylabel('radians'); title('Phase Response');
set(gca, 'XTickMode', 'manual', 'XTick', [-8, -3.8, 0, 3.2, 3.8, 8]);
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 8.21 Digital Chebyshev-I lowpass')
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(' frequency in \pi units'); ylabel('|H|'); title('Magnitude Response');
set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.8, 0.95, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.0056, 0.9441, 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, 0.8, 0.95, 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, 0.8, 0.95, M]);
set(gca, 'YTickMode', 'manual', 'YTick', [-60, -45, -1, 0]);
set(gca,'YTickLabelMode','manual','YTickLabel',['60';'45';' 1';' 0']);
 
subplot(2,2,4); plot(ww/pi, grd); grid on; %axis([0, M, 0, 35]);
xlabel('frequency in \pi units'); ylabel('Samples'); title('Group Delay');
set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.8, 0.95, M]);
%set(gca, 'YTickMode', 'manual', 'YTick', [0:5:35]);
 
figure('NumberTitle', 'off', 'Name', 'Problem 8.21 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 8.21 Imp & Freq Response')
set(gcf,'Color','white');
t = [0:0.01:60]; subplot(2,1,1); impulse(cs,ds,t); grid on;   % Impulse response of the analog filter
axis([0,60,-0.5,1.0]);hold on
 
n = [0:1:60/T]; hn = filter(b,a,impseq(0,0,60/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'); text(0.6,1.05,'Digital filter');

　　运行结果：

通带、阻带指标

模拟Chebyshev-1型低通系统函数，串联形式系数

脉冲响应不变法，转换成数字低通，系统函数直接形式系数

模拟Chebyshev-1型低通，幅度谱、相位谱和脉冲响应

数字Chebyshev-1型低通，幅度谱、相位谱和群延迟