iir_df_bw.m

巴特沃斯滤波器的实现 数字滤波器是通过一定的计算程序减少有用信号中干扰所占比重故实际上它是一种程序滤波。

function Hz_ejw = IIR_DF_BW(Ucd,Ap,Usd,As,t,sum)
% 巴特沃思滤波器
E = (10^(0.1*Ap)-1)^0.5;
V = (10^(0.1*As)-1)^0.5;
Wc = Ucd*t;
Ws = Usd*t;
Ucd = Wc/t; 
Usd = Ws/t;
Uca = (2/t)*tan(Ucd*t/2); Usa=(2/t)*tan(Usd*t/2);
N = ceil(log10(V/E)/log10(Usa/Uca));
k = [1:2*N];
Spk = exp(j*(pi/2+(2*k-1)/(2*N)*pi));
i = find(real(Spk)<0);
Sk(1:N) = Spk(i);
den = real(poly(Sk'));
k0 = polyval(den,0);
disp('模拟巴特沃思滤波器的归一化统函数 Ha(s) 为')
tf(k0,den)
%-----------------------------------------------%
syms s z T;
den_jU = 1;
s = s/Uca;
for i=1:N
den_jU = s^(N-i+1)*den(i)+den_jU;
end 
Ha_s = simple(1/den_jU);
H_z = subs(Ha_s,'s',(2/T)*((1-1/z)/(1+1/z)));
k = 1:sum;
w = (2*pi/sum)*k;
ejw = exp(j*w);
Hz_ejw = subs(H_z,{z,T},{ejw,t*ones(1,length(ejw))});
figure(1),plot(w,abs(Hz_ejw)); grid on
title('巴特沃思低通滤波器')
axis([2*pi/sum,pi,-0.2,1.2*max(abs(Hz_ejw))])