% 第八章: 例 8.21
%            巴特沃思低通濾波器設(shè)計(jì)
%                 BUTTER函數(shù)的應(yīng)用
%
% 數(shù)字濾波器指標(biāo):
wp = 0.2*pi;                         % 數(shù)字通帶頻率(弧度)
ws = 0.3*pi;                         % 數(shù)字阻帶頻率(弧度)
Rp = 1;                              % 通帶波動(dòng)(dB)
As = 15;                             % 阻帶衰減(dB) 

% 模擬原型指標(biāo)
T = 1;                            % 置 T=1
OmegaP = (2/T)*tan(wp/2);            % 預(yù)修正原型通帶頻率
OmegaS = (2/T)*tan(ws/2);            % 預(yù)修正原型阻帶頻率
ep = sqrt(10^(Rp/10)-1);             % 通帶波動(dòng)參數(shù)
Ripple = sqrt(1/(1+ep*ep));          % 通帶波動(dòng)
Attn = 1/(10^(As/20));               % 阻帶衰減

%模擬原型階次計(jì)算
N =ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(OmegaP/OmegaS)));
fprintf('\n*** 巴特沃思濾波器階次 = %2.0f \n',N)
%%*** 巴特沃思濾波器階次 =  6 
OmegaC = OmegaP/((10^(Rp/10)-1)^(1/(2*N))); %模擬原型帶寬截止頻率
wn = 2*atan((OmegaC*T)/2);                %數(shù)字帶寬截止頻率

% 數(shù)字巴特沃思濾波器設(shè)計(jì):
wn = wn/pi;                           %以pi為單位的數(shù)字巴特沃斯截止頻率
[b,a]=butter(N,wn);
[b0,B,A] = dir2cas(b,a)
%%C = 5.7969e-004
%%B = 1.0000    2.0297    1.0300
%%    1.0000    1.9997    1.0000
%%    1.0000    1.9706    0.9709
%%A = 1.0000   -0.9459    0.2342
%%    1.0000   -1.0541    0.3753
%%    1.0000   -1.3143    0.7149