《DSP using MATLAB》Problem 8.22

╰+哭是因爲堅強的太久メ 2021-11-24 01:46 188阅读 0赞

时光飞逝，亲朋会一个一个离我们远去，孤独漂泊一阵子后，我们自己也要离开，

![348130-20190710101852845-2065197297.jpg][]

![348130-20190710101925221-1553833632.png][]

代码：

%% ------------------------------------------------------------------------
    %%            Output Info about this m-file
    fprintf('\n***********************************************************\n');
    fprintf('        <DSP using MATLAB> Problem 8.22 \n\n');
    
    banner();
    %% ------------------------------------------------------------------------
    
    % -------------------------------
    %       ω = ΩT = 2πF/fs
    % Digital Filter Specifications:
    % -------------------------------
    wp = 0.4*pi;                     % digital passband freq in rad/sec
    ws = 0.6*pi;                     % digital stopband freq in rad/sec
    Rp = 0.5;                        % 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
    
    % Analog prototype specifications: Inverse Mapping for frequencies
    T = 2;                       % set T = 1
    Fs = 1/T;
    OmegaP = wp/T;               % prototype passband freq
    OmegaS = ws/T;               % prototype stopband freq
    
    % Analog Butterworth Prototype Filter Calculation:
    [cs, ds] = afd_butt(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, 0.5*pi);
    
    % 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 8.22 Analog Butterworth lowpass')
    set(gcf,'Color','white'); 
    M = 1;                          % Omega max
    
    subplot(2,2,1); plot(ww_s, mag_s/T);  grid on; axis([-M, M, 0, 1.2]);
    xlabel(' Analog frequency in \pi units'); ylabel('|H|'); title('Magnitude in Absolute');
    set(gca, 'XTickMode', 'manual', 'XTick', [-0.3, -0.2, 0, 0.2, 0.3, 0.4, 0.6]);
    set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.0032, 0.5, 0.9441, 1]);
    
    subplot(2,2,2); plot(ww_s, db_s);  grid on; %axis([0, M, -50, 10]);
    xlabel('Analog frequency in \pi units'); ylabel('Decibels'); title('Magnitude in dB ');
    set(gca, 'XTickMode', 'manual', 'XTick', [-0.3, -0.2, 0, 0.4, 0.6]);
    set(gca, 'YTickMode', 'manual', 'YTick', [-65, -50, -1, 0]);
    set(gca,'YTickLabelMode','manual','YTickLabel',['65';'50';' 1';' 0']);
    
    subplot(2,2,3); plot(ww_s, pha_s/pi);  grid on; axis([-M, M, -1.2, 1.2]);
    xlabel('Analog frequency in \pi nuits'); ylabel('radians'); title('Phase Response');
    set(gca, 'XTickMode', 'manual', 'XTick', [-0.3, -0.2, 0, 0.4, 0.6]);
    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 8.22 Digital Butterworth 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, 0.4, 0.6, 1.0, M]);
    set(gca, 'YTickMode', 'manual', 'YTick', [0, 0.0032, 0.5, 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, 0.4, 0.6, 1.0, M]);
    set(gca, 'YTickMode', 'manual', 'YTick', [-1:1:1]);
    
    subplot(2,2,3); plot(ww/pi, db); axis([0, M, -100, 10]); grid on;
    xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude in dB ');
    set(gca, 'XTickMode', 'manual', 'XTick', [0, 0.4, 0.6, 1.0, M]);
    set(gca, 'YTickMode', 'manual', 'YTick', [-70, -50, -1, 0]);
    set(gca,'YTickLabelMode','manual','YTickLabel',['70';'50';' 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, 0.4, 0.6, 1.0, M]);
    %set(gca, 'YTickMode', 'manual', 'YTick', [0:5:35]);
    
    figure('NumberTitle', 'off', 'Name', 'Problem 8.22 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 8.22 Imp & Freq Response')
    set(gcf,'Color','white'); 
    t = [0:0.01:80]; subplot(2,1,1); impulse(cs,ds,t); grid on;   % Impulse response of the analog filter
    axis([0,80,-0.2,0.3]);hold on
    
    n = [0:1:80/T]; hn = filter(b,a,impseq(0,0,80/T));           % Impulse response of the digital filter
    stem(n*T,hn); xlabel('time in sec'); title ('Impulse Responses');
    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*Fs,'b+', wwz/(2*pi)*Fs,magz,'r'); grid on;
    
    xlabel('frequency in Hz'); title('Magnitude Responses'); ylabel('Magnitude'); 
    
    text(-0.3,0.15,'Analog filter'); text(0.4,0.55,'Digital filter');

运行结果：

通带、阻带绝对指标

![348130-20190710102030718-261230001.png][]

模拟原型butterworth低通滤波器直接形式系数

![348130-20190710102105574-367136180.png][]

模拟原型butterworth低通滤波器串联形式系数

![348130-20190710102124324-1199616178.png][]

脉冲响应不变法，模拟低通转换成数字低通，并联形式系数

![348130-20190710102136686-453046973.png][]

![348130-20190710102210410-1302160980.png][]

![348130-20190710102226450-201197707.png][]

![348130-20190710102248417-2005081314.png][]

转载于:https://www.cnblogs.com/ky027wh-sx/p/11162249.html

[348130-20190710101852845-2065197297.jpg]: /images/20211122/909035ba01104af9ac3eba4aef0392c9.png
[348130-20190710101925221-1553833632.png]: /images/20211122/da220e301f43474093fc4e7e86cbdb0b.png
[348130-20190710102030718-261230001.png]: /images/20211122/be68ad356e3440d287fe3c176ef17227.png
[348130-20190710102105574-367136180.png]: /images/20211122/1cd1a69c5c074a859821382adca8278c.png
[348130-20190710102124324-1199616178.png]: /images/20211122/f0f3206e6c564746bac7ada6f6a90d2b.png
[348130-20190710102136686-453046973.png]: /images/20211122/ed4bea9399ce4a399c2135b705fc975c.png
[348130-20190710102210410-1302160980.png]: /images/20211122/766bf973045849838b8ac6dd9c233b64.png
[348130-20190710102226450-201197707.png]: /images/20211122/9916fea5d7224ad38e70e15fa8ee3dc3.png
[348130-20190710102248417-2005081314.png]: /images/20211122/c7b0bdc458274a3890d800c5cf96fb01.png