ex081700.m

Digital signal processing using Matlab一書之範例程式

% Chapter 8: Example 8.17
%            BiLinear Transformation:
%                Butterworth Lowpass Filter Design
%
% Digital Filter Specifications:
wp = 0.2*pi;                         % digital Passband freq in Hz
ws = 0.3*pi;                         % digital Stopband freq in Hz
Rp = 1;                              % Passband ripple in dB
As = 15;                             % Stopband attenuation in dB

% Analog Prototype Specifications: Inverse mapping for frequencies
T = 1; Fs = 1/T;                     % Set T=1
OmegaP = (2/T)*tan(wp/2);            % Prewarp Prototype Passband freq
OmegaS = (2/T)*tan(ws/2);            % Prewarp Prototype Stopband freq
ep = sqrt(10^(Rp/10)-1);             % Passband Ripple parameter
Ripple = sqrt(1/(1+ep*ep));          % Passband Ripple
Attn = 1/(10^(As/20));               % Stopband Attenuation

% Analog Butterworth Prototype Filter Calculation:
[cs,ds] = afd_butt(OmegaP,OmegaS,Rp,As);
%%*** Butterworth Filter Order =  6 

% Bilinear transformation:
[b,a] = bilinear(cs,ds,T);
[C,B,A] = dir2cas(b,a)
%%C = 5.7969e-004
%%B = 1.0000    2.0183    1.0186
%%    1.0000    1.9814    0.9817
%%    1.0000    2.0004    1.0000
%%A = 1.0000   -0.9459    0.2342
%%    1.0000   -1.0541    0.3753
%%    1.0000   -1.3143    0.7149

% Plotting
figure(1); subplot(1,1,1)
[db,mag,pha,grd,w] = freqz_m(b,a);
subplot(2,2,1); plot(w/pi,mag); title('Magnitude Response')
xlabel('frequency in pi units'); ylabel('|H|'); axis([0,1,0,1.1])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[0,Attn,Ripple,1]); grid
subplot(2,2,3); plot(w/pi,db); title('Magnitude in dB');
xlabel('frequency in pi units'); ylabel('decibels'); axis([0,1,-40,5]);
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[-50,-15,-1,0]); grid
set(gca,'YTickLabelMode','manual','YTickLabels',['50';'15';' 1';' 0'])
subplot(2,2,2); plot(w/pi,pha/pi); title('Phase Response')
xlabel('frequency in pi units'); ylabel('pi units'); axis([0,1,-1,1]);
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[-1,0,1]); grid
subplot(2,2,4); plot(w/pi,grd); title('Group Delay')
xlabel('frequency in pi units'); ylabel('Samples'); axis([0,1,0,10])
set(gca,'XTickMode','manual','XTick',[0,0.2,0.3,1]);
set(gca,'YTickmode','manual','YTick',[0:2:10]); grid