《DSP using MATLAB》Problem 7.10

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 7.10 \n\n');
 
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
wp1 = 0.3*pi; ws1 = 0.4*pi; ws2 = 0.6*pi; wp2 = 0.7*pi;
As = 50; Rp = 0.2;
tr_width = min( ws1-wp1, wp2-ws2 );
M = ceil(6.6*pi/tr_width) + 1;                 % Hamming Window
fprintf('\nFilter Length is %d.\n', M);
 
n = [0:1:M-1];  wc1 = (ws1+wp1)/2; wc2 = (wp2+ws2)/2;
 
%wc = (ws + wp)/2,                    % ideal LPF cutoff frequency
 
hd = ideal_lp(wc1, M) + ideal_lp(pi, M) - ideal_lp(wc2, M);
w_ham = (hamming(M))';  h = hd .* w_ham;
[db, mag, pha, grd, w] = freqz_m(h, [1]);  delta_w = 2*pi/1000;
[Hr,ww,P,L] = ampl_res(h);
 
Rp = -(min(db(1 : 1 : wp1/delta_w+1)));             % Actual Passband Ripple
fprintf('\nActual Passband Ripple is %.4f dB.\n', Rp);
 
As = -round(max(db(ws1/delta_w+1 : 1 : ws2/delta_w)));        % Min Stopband attenuation
fprintf('\nMin Stopband attenuation is %.4f dB.\n', As);
 
[delta1, delta2] = db2delta(Rp, As)
 
%Plot
 
figure('NumberTitle', 'off', 'Name', 'Problem 7.10 ideal_lp Method')
set(gcf,'Color','white'); 
 
subplot(2,2,1); stem(n, hd); axis([0 M-1 -0.2 0.8]); grid on;
xlabel('n'); ylabel('hd(n)'); title('Ideal Impulse Response');
subplot(2,2,2); stem(n, w_ham); axis([0 M-1 0 1.1]); grid on;
xlabel('n'); ylabel('w(n)'); title('Hamming Window');
subplot(2,2,3); stem(n, h); axis([0 M-1 -0.2 0.8]); grid on;
xlabel('n'); ylabel('h(n)'); title('Actual Impulse Response');
 
subplot(2,2,4); plot(w/pi, db); axis([0 1 -120 10]); grid on;
set(gca,'YTickMode','manual','YTick',[-90,-50,0]);
set(gca,'YTickLabelMode','manual','YTickLabel',['90';'50';' 0']);
set(gca,'XTickMode','manual','XTick',[0,0.3,0.4,0.6,0.7,1]);
xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude Response in dB');
 
figure('NumberTitle', 'off', 'Name', 'Problem 7.10 h(n) ideal_lp Method')
set(gcf,'Color','white'); 
 
subplot(2,2,1); plot(w/pi, db); grid on; axis([0 1 -120 10]);
set(gca,'YTickMode','manual','YTick',[-90,-50,0])
set(gca,'YTickLabelMode','manual','YTickLabel',['90';'50';' 0']);
set(gca,'XTickMode','manual','XTick',[0,0.3,0.4,0.6,0.7,1]);
xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude Response in dB');
 
subplot(2,2,3); plot(w/pi, mag); grid on; %axis([0 1 -100 10]);
xlabel('frequency in \pi units'); ylabel('Absolute'); title('Magnitude Response in absolute');
set(gca,'XTickMode','manual','XTick',[0,0.3,0.4,0.6,0.7,1,1.3,1.4,1.6,1.7,2]);
set(gca,'YTickMode','manual','YTick',[0,1.0]);
 
subplot(2,2,2); plot(w/pi, pha); grid on; %axis([0 1 -100 10]);
xlabel('frequency in \pi units'); ylabel('Rad'); title('Phase Response in Radians');
subplot(2,2,4); plot(w/pi, grd*pi/180);  grid on; %axis([0 1 -100 10]);
xlabel('frequency in \pi units'); ylabel('Rad'); title('Group Delay');
 
figure('NumberTitle', 'off', 'Name', 'Problem 7.10 h(n)')
set(gcf,'Color','white'); 
 
plot(ww/pi, Hr); grid on; %axis([0 1 -100 10]);
xlabel('frequency in \pi units'); ylabel('Hr'); title('Amplitude Response');
set(gca,'YTickMode','manual','YTick',[-0.0032, 0,0.0032, 0.9975, 1,1.0025]);
%set(gca,'YTickLabelMode','manual','YTickLabel',['90';'45';' 0']);
%set(gca,'XTickMode','manual','XTick',[0,0.2,0.35,0.55,0.75,1,1.2,1.35,1.55,1.75,2]);

　　运行结果：

阻带最小衰减为50dB，满足设计要求。

用Hamming窗设计的滤波器脉冲响应，其幅度响应（dB和Absolute单位）、相位响应和群延迟响应。

振幅响应（Absolute单位）

通带部分

阻带部分